(Select all that are correct) which statements describe key features of function g if g(x) = f(x + 2)
a. y-intercept at (0,4)
b. domain of {x|-♾️< x <♾️}
c. horizontal asymptote of y = 0
d. horizontal asymptote of y=2
e. y-intercept at (0,1)
Answers
Answer:
Y-intercept (0,1) / Domain (-infinite,infinite) / horizontal asymptote y=0
The y-intercept is: (0,1)
The domain is [tex]\{x|-\infty < x < \infty\}[/tex]
The horizontal asymptote is [tex]y = 0[/tex]
The given parameters from the complete question are:
[tex]f(x) = 2^{x-2}[/tex]
[tex]g(x) = f(x + 2)[/tex]
First, we calculate the function of g(x)
[tex]g(x) = f(x + 2)[/tex]
Calculate f(x + 2)
[tex]f(x) = 2^{x-2}[/tex]
[tex]f(x + 2) = 2^{x+2-2}[/tex]
[tex]f(x + 2) = 2^x[/tex]
So:
[tex]g(x) = 2^x[/tex]
Start by calculating the y intercept:
This means, we calculate the g(x) when [tex]x=0[/tex]
[tex]g(x) = 2^x[/tex]
[tex]g(0) = 2^0[/tex]
[tex]g(0) =1[/tex]
The above computation means (a) is incorrect; but (e) is correct.
Next, calculate the domain of g(x)
[tex]g(x) = 2^x[/tex]
Some features in a function that limit the x values are: roots, fractions, etc.
[tex]g(x) = 2^x[/tex] does not have any restricting value of x.
This means the value of x ranges from negative infinity to positive infinity.
Hence, the domain is: [tex](-\infty,\infty)[/tex]
The above computation means (b) is correct
Next, calculate the horizontal asymptote.
To do this, we plot the graph of g(x) --> see attachment
Then we trace a horizontal line from the horizontal part of the curve of g(x) till it gets to the y-axis.
From the attached graph of g(x), the line touches the y-axis at [tex]y = 0[/tex]
So, the horizontal asymptote is: [tex]y = 0[/tex]
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Related Questions
Given that [tex](ax+4)(2x+b)=2x^2+5x-12[/tex], what are the values of a and b?
Answers
Answer:
a = 1, b = - 3
Step-by-step explanation:
Expand the factors on the left side, then compare the coefficients of like terms on both sides.
left side
(ax + 4)(2x + b) ← expand using FOIL
= 2ax² + abx +8x + 4b
= 2ax² + x(ab + 8) + 4b
Compare coefficients of like terms with those on right side.
coefficients of x² terms
2a = 2 ( divide both sides by 2 )
a = 1
comparing constant terms
4b = - 12 ( divide both sides by 4 )
b = - 3
HELP PLS this is my last question
Answers
Answer:
The solutions to the system of the equations are:
[tex]y=1,\:x=3[/tex]
Step-by-step explanation:
Given the equations
[tex]y=\frac{2}{3}x-1;\:y=-x+4[/tex]
solving the system of equation
[tex]\begin{bmatrix}y=\frac{2}{3}x-1\\ y=-x+4\end{bmatrix}[/tex]
Arrange equation variables for elimination
[tex]\begin{bmatrix}y-\frac{2}{3}x=-1\\ y+x=4\end{bmatrix}[/tex]
[tex]y+x=4[/tex]
[tex]-[/tex]
[tex]\underline{y-\frac{2}{3}x=-1}[/tex]
[tex]\frac{5}{3}x=5[/tex]
[tex]\begin{bmatrix}y-\frac{2}{3}x=-1\\ \frac{5}{3}x=5\end{bmatrix}[/tex]
solving for x
[tex]\frac{5}{3}x=5[/tex]
[tex]5x=15[/tex]
Divide both sides by 15
[tex]\frac{5x}{5}=\frac{15}{5}[/tex]
[tex]x=3[/tex]
[tex]\mathrm{For\:}y-\frac{2}{3}x=-1\mathrm{\:plug\:in\:}x=3[/tex]
[tex]y-\frac{2}{3}\cdot \:3=-1[/tex]
[tex]y-2=-1[/tex]
Add 2 to both sides
[tex]y-2+2=-1+2[/tex]
[tex]y=1[/tex]
Therefore, the solutions to the system of the equations are:
[tex]y=1,\:x=3[/tex]
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BD=16 and ÁT is the
perpendicular bisector of BD
BC=
Answers
Answer:
8
Step-by-step explanation:
16/2=8
Answer:
8
Step-by-step explanation:
A bisector bisects a line in HALF. Thus, by dividing 16 in half you will get BC=8.
please help
answer choices are:
a (-2,-8)
b (2,-8)
c (2,-4)
d. (-2,4)
Answers
By the square property, if b is a real number , and a2=b, then a=
Answers
Answer:
[tex]a=\sqrt{6},\:a=-\sqrt{6}[/tex]
Step-by-step explanation:
Given
b is a real number[tex]a^2=b[/tex]as
[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]
so
[tex]a^2=6[/tex]
[tex]a=\sqrt{b},\:a=-\sqrt{b}[/tex]
Therefore,
[tex]a=\sqrt{6},\:a=-\sqrt{6}[/tex]
Answer:
lal
Step-by-step explanation:
ap3x
please yall im crying this is hard
Answers
Answer:
I think ur and is 4140. but I'm not sure, sorry if its incorrect.
What is the range of the relation below?
Answers
Answer:
D.
Step-by-step explanation:
because the lowest y is -3 and the highest is 2
6p = 3p + 2p + p is true for
Answers
Answer:
For any value
Step-by-step explanation:
Answer:
Anything substituted for p should be correct
Step-by-step explanation:
Suppose IQ scores were obtained from randomly selected couples. For 20 such pairs of people, the linear correlation coefficient is 0.907 and the equation of the regression line is y=9.88+0.9x, where x represents the IQ score of the husband. What is the best predicted IQ of the wife, given that the husband has an IQ of 101?
Answers
Answer:
108.88
Step-by-step explanation:
Given that:
Equation of Regression line obtained for couple's IQ:
y=9.88+0.9x
x represents the IQ score of the husband
The best predicted IQ of wife Given that husband's IQ is 110
y = 9.88 + 0.9(110)
y = 9.88 + 99
y = 108.88
Mole Conversion:
What is the mass of 3.13 x 1023 molecules of carbon dioxide?
Answers
Answer:
The mass of 3.13*10²³ molecules of carbon dioxide is 22.88 g.
Step-by-step explanation:
Avogadro's Number or Avogadro's Constant is the number of particles that make up a substance (usually atoms or molecules) and that can be found in the amount of one mole of said substance. Its value is 6.023*10²³ particles per mole and it applies to any substance.
Then you can apply the following rule of three: if 6.023*10²³ molecules are present in 1 mole, 3.13*10²³ molecules are present in how many moles?
[tex]moles=\frac{3.13*10^{23}molecules*1 mole }{6.023*10^{23}molecules}[/tex]
moles= 0.52
Since the molar mass of carbon dioxide is 44 g / mole, then the following rule of three can be applied: if there are 44 g in 1 mole, how much mass is there in 0.52 moles?
[tex]mass=\frac{0.52 moles*44 g}{1 mole}[/tex]
mass= 22.88 g
The mass of 3.13*10²³ molecules of carbon dioxide is 22.88 g.
PLEASE HELP MEEEEE!!! IT's TIMED
Answers
Answer:
x is less than oe equal to 12
Answer:
x ≤ 15
Step-by-step explanation:
7x - 6 ≤ 3x + 54
Subtract 3x from both sides;
4x - 6 ≤ 54
Add 6 to both sides;
4x ≤ 60
Divide both sides by 4;
x ≤ 15
What is a common tip percentage amount that people receive?
Answers
Answer:
15-20%
Step-by-step explanation:
can u make me brainiest thanks
A parking lot that has 520 spaces
was filled with 390 cars. What
percent of the parking lot was full?
Answers
Answer:
75%
Step-by-step explanation:
390/520 = 0.75 =75
hope that helps ;)
Answer:
75%
Step-by-step explanation:
390/520×100%
0.75×100%
75%
Factor 14x−24 using the GCF
Please help me! Hurry! Please show your work.
Answers
Answer:
2(7x - 12)
Step-by-step explanation:
Find the GCF of 14 and 24: 2Divide each number by 2 shown in steps 3 and 414x ÷ 2 = 7x24 ÷ 2 = 12Re-write the expression: 2(7x - 12)I hope this helps!
Find the square of each imaginary number.
(Get rid of the i)
Answers
Answer:
- 32/21 over 5 is
Step-by-step explanation:
*gets coins and runs to the store to get "milk"
Answer:
-765/25
Step-by-step explanation:
Ella is putting her savings into a retirement fund that will compound her $7000 semiannually at 7% interest. How much will her retirement fund be worth after 10 years? *
Answers
Answer:
8099
Step-by-step explanation:
LaShea would like to invest her $100 in birthday money. Which option will give her the most money at the end of the investment period?
1 year at 8 percent
1.5 years at 7 percent
2 years at 6.5 percent
3 years at 4 percent
Answers
Answer:
1 year at 8 percent
Step-by-step explanation:
i took the test
) Solve this equation: − 10 + = 8 + 2 − 18
Answers
Answer:
I think the question is wrong check ur question and I will answer
Morag typed 60 words in one minute. Express as a unit rate.
Answers
Answer:
60 words per minute...60/1...this is already in unit rate form
y=-4/7x+2 is it Proportional
Constant of proportionality: k=
Not proportional
URGENT
Answers
Answer:
It is
5/7
Explanation:
The number
5/7
tells you that when
x
increases of
1
then
y
always increases of
5/7
.
Graphically:
graph{7/7*x [-10, 10, -5, 5]}
Step-by-step explanation:
factor completely, 0.2x + 0.8 a. x b. 0.8(x + 1) c. 0.2(x + 1) d. 0.2(x + 4)
Answers
Answer:
d. 0.2 ( x + 4 )
Step-by-step explanation:
0.2x + 0.8
Both 0.2x and 0.8 have a common factor of 0.2, hence pull 0.2 out.
0.2x + 0.8
0.2 ( x + 4 )
Will give brainlyest Will give brainlyest Will give brainlyest Will give brainlyest Will give brainlyest.idk and if you give me the answer can you tell me if I put it on the far right or left
Answers
Answer:
so i tried to draw it.
Step-by-step explanation:
Answer:
left
Step-by-step explanation:
plz i need 4 more brainlyests to pass
Quickly XD!
3 friends share 2 pizzas evenly.
About how much pizza will each friend get?
Sorry if you tryna enjoy your weekend I Needa get this done.
Answers
y=2/3 orange for each friend (decimal: 0.6667 rounded to 4d. p)
PREMISES
y=the fraction of 2 oranges that each of 3 friends shares equally
CALCULATIONS
To distribute 2 oranges equally between 3 friends requires that the oranges be sliced proportionately equal to the number of friends which is 3
So, then,
y=
Each friend receives 1/3 of each of 2 oranges making 2/3 orange for each friend.
If y=2/3 orange, then the equations
3*2/3 orange=2 oranges
6/3 oranges=2 oranges and
2 oranges=2 oranges prove the solution y=2/3 orange to the fraction of 2 oranges shared by each of 3 friends
What is x-2+5x
What is -4x-10+6x
What is 7+10x+4x-8
Answers
Answer:
What is x-2+5x = 6x-2
What is -4x-10+6x = 2x-10
What is 7+10x+4x-8 = -4x+9
Step-by-step explanation:
A pre-image arrow pointing east is rotated 135° clockwise. In which direction is the image arrow pointin
Answers
Given :
A pre-image arrow pointing east is rotated 135° clockwise.
To Find :
In which direction is the image arrow point.
Solution :
90° clockwise shift make it south.
Now, remaining angle for rotation ( 135 - 90 )° = 45°.
So, direction of moving 45° more clockwise makes it 45° west of south or 45° south of west.
Hence, this is the required solution.
7
Which two whole numbers is 20 between?
Answers
Answer:
19 and 21
Step-by-step explanation:
... 17, 18, 19 , 20, 21, 22, 23 ,24, 25
PLS HELP! DUE TODAY! I WILL GIVE BRAINLIEST!
In the following activity, match each pair of equivalent expressions.
3(x + 5)
9x - 2(3x - 3)
(x + 14) - (8 - 2x)
(7 - 2x) + (3x - 11)
(7 + 5x) + (-4x - 1)
-2x + 9 + 5x + 6
-4(x + 1) + 5x
-7 + 6x - 4x + 3
2(x - 2)
-3x + 6 + 4x
Answers
Answer:
Matches are:
1 and 6
2 and 3
4 and 7
5 and 10
8 and 9
Step-by-step explanation:
First just expand all:
1. 3x + 15
2. 3x + 6
3. 3x +6
4. x - 4
5. x + 6
6. 3x +15
7. x - 4
8. 2x - 4
9. 2x - 4
10. x + 6
Please give brainliest! Thanks, hope this helps!
solve for x 5(4x-5)+3x-1=20
Answers
Step-by-step explanation:
20x-25+3x-1=20
20x+3x=20+25+1
23x=46
X=2
Answer:
x=2
Step-by-step explanation:
5(4x-5)+3x-1=20 (given)
20x - 25 + 3x -1 = 20 (distribute)
23x -26 = 20 (combine like terms)
23x = 46 (add)
x=2 (division)
Please help is this a solution or inequality 5-x<8;x=-3
Answers
Answer:
Its a inequality
Step-by-step explanation:
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The two expressions we have is ‘5 - x’ and ‘8’. If X is equal to three, then we get ‘5 - 3’ and ‘8’. This comes out to 2 > 8.
Hope this helps :)
what is the common fraction of the decimal 0,76
Answers
Answer:
76/100
Step-by-step explanation: 76 is in the hundreds place