$$\lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n$$

Question 1

Which of the following best describes the domain and range of the exponential function $$f(x) = 3^x$$?

Accepted Answer

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

Question 2

If $$f(x) = a^x$$ with $$0 \u003c a \u003c 1$$, which statement is true about the graph of $$f$$?

Accepted Answer

The graph is decreasing and has a horizontal asymptote at $$y = 0$$

Question 3

Evaluate $$3^{1.7}$$ using a calculator. Which value is closest?

Accepted Answer

$$6.704991854$$

Question 4

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

Accepted Answer

Product of powers property

Question 5

The number $$e is $$defined by which of the following limits?

Accepted Answer

$$\lim_{n 	o \infty} \left(1 + \frac{1}{n}ight)^n$$

Question 6

Which of the following is the y-intercept of the function $$f(x) = 3$$^{-x}$$ + 1$$?

Accepted Answer

$$(0, 2)$$

Question 7

What is the horizontal asymptote of the function $$f(x) = -e^x + 2$$?

Accepted Answer

$$y = 0$$

Question 8

Solve the exponential equation $$2^{x+2} = 8$. What is the value of x$?

Accepted Answer

$$x = 1$$

Question 9

Which of the following statements is true for the exponential function $$f(x) = a^x$$ where $$a \u003e 1$$?

Accepted Answer

The function is one-to-one and increasing.

Question 10

If $$f(x) = e^x$$, what is $$f(-2)$$ rounded to two decimal places?

Accepted Answer

$$0.14$$

Question 11

Which transformation is applied to $$y = e^x to $$obtain $$y = -e^x$$?

Accepted Answer

Reflection over the x-axis

Question 12

If $$a^u = a^v$$, what can be concluded?

Accepted Answer

$$u = v$$

Question 13

Which of the following is the initial value of the exponential function $$f(x) = C a^x$$?

Accepted Answer

$$C$$

Question 14

What is the value of $$e^2$$ rounded to two decimal places?

Accepted Answer

$$7.39$$

Question 15

Which of the following is NOT a property of the exponential function $$f(x) = a^x$$ for $$a \u003e 1$$?

Accepted Answer

The graph has an x-intercept.

Question 16

Solve the exponential equation $$9^{2x-5} = 27^x$. What is the value of x$?

Accepted Answer

$$x = 1$$

Question 17

Which of the following best describes the range of $$f(x) = -e^x + 2$$?

Accepted Answer

$$(-\infty, 2)$$

Question 18

If $$f(x) = \left(\frac{1}{3}\right)^x$$, what is $$f(-2)$$?

Accepted Answer

$$9$$

Question 19

Which real-world scenario best models exponential growth?

Accepted Answer

The population of bacteria doubling every hour

Question 20

Solve the equation $$e^{2x-5}$$ = $$e^{x-6}. $$What is the value of $$x$$?

Accepted Answer

$$x = -1$$

Exponential Functions: Properties, Graphs, and Applications

스터디 가이드 - 연습 문제