(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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Answer:
D.
Step-by-step explanation:
because the lowest y is -3 and the highest is 2
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Step-by-step explanation:
16/2=8
Answer:
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Step-by-step explanation:
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A pre-image arrow pointing east is rotated 135° clockwise. In which direction is the image arrow pointin
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Given :
A pre-image arrow pointing east is rotated 135° clockwise.
To Find :
In which direction is the image arrow point.
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90° clockwise shift make it south.
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what is the common fraction of the decimal 0,76
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Which two whole numbers is 20 between?
Answers
Answer:
19 and 21
Step-by-step explanation:
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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?
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What is a common tip percentage amount that people receive?
Answers
Answer:
15-20%
Step-by-step explanation:
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y=-4/7x+2 is it Proportional
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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:
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:
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20x - 25 + 3x -1 = 20 (distribute)
23x -26 = 20 (combine like terms)
23x = 46 (add)
x=2 (division)
) Solve this equation: − 10 + = 8 + 2 − 18
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Answer:
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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
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so
[tex]a^2=6[/tex]
[tex]a=\sqrt{b},\:a=-\sqrt{b}[/tex]
Therefore,
[tex]a=\sqrt{6},\:a=-\sqrt{6}[/tex]
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lal
Step-by-step explanation:
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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)
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y = 108.88
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
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Answer:
so i tried to draw it.
Step-by-step explanation:
Answer:
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A parking lot that has 520 spaces
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Answers
Answer:
75%
Step-by-step explanation:
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Answer:
75%
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390/520×100%
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Answer:
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Step-by-step explanation:
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Add 6 to both sides;
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Answer:
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Answers
Answer:
For any value
Step-by-step explanation:
Answer:
Anything substituted for p should be correct
Step-by-step explanation:
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Answers
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Answers
Answer:
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0.2x + 0.8
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About how much pizza will each friend get?
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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
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y=
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If y=2/3 orange, then the equations
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6/3 oranges=2 oranges and
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Answer:
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Step-by-step explanation:
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Answer:
Its a inequality
Step-by-step explanation:
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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
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= 2ax² + abx +8x + 4b
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In the following activity, match each pair of equivalent expressions.
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Answers
Answer:
Matches are:
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4 and 7
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Step-by-step explanation:
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2. 3x + 6
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Please help me! Hurry! Please show your work.
Answers
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2(7x - 12)
Step-by-step explanation:
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Answer:
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What is 7+10x+4x-8 = -4x+9
Step-by-step explanation:
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Answer:
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Answer:
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Step-by-step explanation:
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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]
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