Question 1

Which of the following best describes the end behavior of the exponential function $$f(x) = 2^x as$$ $$x 	o -\infty$$?

Accepted Answer

$$f(x) 	o 0$$

Question 2

What is the horizontal asymptote of the function $$f(x) = \left( \frac{1}{3} \right)^x$$?

Accepted Answer

$$y = 0$$

Question 3

Given $$f(x) = 2^x$$, which transformation results in $$g(x) = 2$$^{x-3}$$ + 4$$?

Accepted Answer

Shift right 3 units and up 4 units

Question 4

Which of the following functions represents a reflection of $$f(x) = 3^x$$ over the $$y-$$axis?

Accepted Answer

$$f(x) = 3$$^{-x}$$

Question 5

If $$f(x) = \left( \frac{1}{2} \right)^x$$, which statement is true about its graph?

Accepted Answer

The graph decreases as $$x$$ increases

Question 6

What is the domain and range of $$f(x) = 2^x$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$(0, \infty)$$

Question 7

Which transformation is applied to $$f(x) = 2^x to $$obtain $$g(x) = -2^x + 3$$?

Accepted Answer

Reflect over $$x-$$axis and shift up 3 units

Question 8

Given $$f(x) = 2^x$$, which of the following is the equation for $$f(x)$$ shifted 2 units left and 5 units down?

Accepted Answer

$$f(x) = 2$$^{x+2}$$ - 5$$

Question 9

Which of the following best describes the range of $$f(x) = -3^x$$?

Accepted Answer

$$(-\infty, 0)$$

Question 10

A population of bacteria triples every hour. If the initial population is 100, which function models the population after $$t$$ hours?

Accepted Answer

$$P(t) = 100 \cdot 3^t$$

Question 11

Which of the following is the correct graph transformation for $$g(x) = 2$$^{-x}$$ + 1$$ from $$f(x) = 2^x$$?

Accepted Answer

Reflect over $$y-$$axis, shift up 1 unit

Question 12

If $$f(x) = 2^x$$, which of the following points is always on the graph?

Accepted Answer

$$(0, 1)$$

Question 13

Which of the following statements is true about the graph of $$f(x) = \left( \frac{1}{4} \right)^x$$?

Accepted Answer

It is a decreasing function

Question 14

What is the effect of the transformation $$g(x) = 2$$^{x+3}$$ on the graph of f(x) = 2^x$?

Accepted Answer

Shift left 3 units

Question 15

Which of the following exponential functions has a horizontal asymptote at $$y = 2$$?

Accepted Answer

$$f(x) = 3^x + 2$$

Question 16

Given $$f(x) = 2^x$$, which function represents a vertical stretch by a factor of 4?

Accepted Answer

$$f(x) = 4 \cdot 2^x$$

Question 17

If $$f(x) = 2^x$$, what is the equation for $$f(x)$$ reflected over the $$x-$$axis and shifted down 2 units?

Accepted Answer

$$f(x) = -2^x - 2$$

Question 18

Which of the following best describes the graph of $$f(x) = 2$$^{-x}$$ compared to f(x) = 2^x$?

Accepted Answer

It is a reflection over the $$y-$$axis

Question 19

A radioactive substance decays so that its mass halves every 5 years. If the initial mass is 80 grams, which function models the mass after $$t$$ years?

Accepted Answer

$$M(t) = 80 \left( \frac{1}{2} \$$right)^{t/5}$$

Graphing and Transformations of Exponential Functions

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