As $$x \to \infty$$, $$f(x) \to 0$$; as $$x \to -\infty$$, $$f(x) \to \infty$$

Question 1

Which of the following is the correct general form of an exponential function?

Accepted Answer

$$f(x) = C a^x$$

Question 2

Given the exponential function $$f(x) = 3 \cdot 2^x$$, what is the initial value?

Accepted Answer

$$3$$

Question 3

What is the domain and range of the function $$f(x) = 5^x$$?

Accepted Answer

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

Question 4

Which of the following best describes the graph of $$f(x) = a^x$$ for $$a \u003e 1$$?

Accepted Answer

It is an increasing function with a horizontal asymptote at $$y = 0.$$

Question 5

Evaluate $$e^{0.57} to $$four decimal places using a calculator.

Accepted Answer

$$1.7720$$

Question 6

Which property of exponents is illustrated by $$a^s \cdot a^t = a$$^{s+t}$$?

Accepted Answer

Product of powers property

Question 7

If $$f(x) = 2^x$$ and $$g(x) = 2x + 1$$, which function is exponential and which is linear?

Accepted Answer

$$f(x) is $$exponential, $$g(x) is $$linear

Question 8

Solve for $$x$$: $$5^{x+3} = 125$

Accepted Answer

$$x = -1$$

Question 9

Which of the following is the value of $$e to $$four decimal places?

Accepted Answer

$$2.7183$$

Question 10

Given the function $$F(t) = 1 - e$$^{-0.1t}$$, what is the probability that a car will arrive within 10 minutes?

Accepted Answer

$$0.6321$$

Question 11

Which of the following points is always on the graph of $$f(x) = a^x$$ for any $$a \u003e 0$$, $$a 
eq 1$$?

Accepted Answer

$$(0, 1)$$

Question 12

If $$a^u = a^v$$ for $$a \u003e 0$$, $$a 
eq 1$$, what can you conclude?

Accepted Answer

$$u = v$$

Question 13

Which of the following best describes the end behavior of $$f(x) = a^x$$ for $$0 \u003c a \u003c 1$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o 0$$; as $$x 	o -\infty$$, $$f(x) 	o \infty$$

Question 14

Which of the following is the horizontal asymptote of $$f(x) = 4^x$$?

Accepted Answer

$$y = 0$$

Question 15

If $$f(x) = 2e$$^{-x}$$, what is the y-intercept of the function?

Accepted Answer

$$2$$

Question 16

Which of the following is a real-world application of exponential functions?

Accepted Answer

Modeling population growth

Question 17

Given $$f(x) = 3 \cdot 4^x$$, which of the following points lies on its graph?

Accepted Answer

$$(1, 12)$$

Question 18

If $$f(x) = 2^x$$ and $$g(x) = 2x$$, which statement is true?

Accepted Answer

$$f(x) is $$exponential, $$g(x) is $$linear

Question 19

Which of the following is the correct value for $$e^4 to $$four decimal places?

Accepted Answer

$$54.5982$$

Exponential Functions: Properties, Graphs, and Applications

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