Question 1

Which graph best represents the exponential function $$f(x) = 6^x$$?

Accepted Answer

Graph with points (2, 36), (1, 6), (0, 1), (-1, 1/6)

Question 2

Which graph best represents the exponential function $$f(x) = \left(\frac{7}{8}\right)^x$$?

Accepted Answer

Graph with points (-1, 8/7), (0, 1), (1, 7/8)

Question 3

Solve the logarithmic equation $$\log_5$(x+5) + \log_5$(x+1) = 2. $$Which value of $$x is $$valid?

Accepted Answer

$$x = -3 + \sqrt{29} \approx 2.385$$

Question 4

Verify the equation $$n^2$$ \$$log_2(2n$$) = $$n^3. Is it $$true? If not, what is the correct statement?

Accepted Answer

False, correct statement should be: $$n^2$$ \$$log_2(2n$$) = $$n^2 n$

Question 5

A wetland area has a hydronium concentration of $$3.89 	imes 10$$^{-7}$$ mol/L. How should it be categorized?

Accepted Answer

Bog

Question 6

For the functions $$f(x) = \log_e x$$ and $$g(x) = -\ln(5x)$$, what are their domains and ranges?

Accepted Answer

Domain $$f(x): x \u003e 0$$, $$g(x): x \u003e 0$$; Range $$f(x)$$ and $$g(x)$$: all real values

Question 7

Solve the exponential equation $$2e^{2x} + 3$$ = \frac{2}{e}$$. What is the value of x$?

Accepted Answer

$$x = -2$$

Question 8

Approximate the value of $$e^{-1.9} to $$four decimal places.

Accepted Answer

0.1496

Question 9

Solve for $$x in $$the logarithmic equation $$\log_{1/5}(x+98) = -3.$$

Accepted Answer

$$\{9\}$$

Question 10

Solve for $$x in $$the equation $$\left(\frac{1}{e}\$$right)^{-3x}$$ = \left(\frac{1}{e^3$}\$$right)^{2x+5}$$.

Accepted Answer

$$x = -\frac{3}{5}$$

Question 11

Which of the following is the logarithmic form of $$b^4 = 1296$?

Accepted Answer

$$\log_b 1296 = 4$$

Question 12

Which of the following is the logarithmic form of $$4^{-3}$$ = \frac{1}{64}$$?

Accepted Answer

$$\log_4$ \frac{1}{64} = -3$$

Question 13

Find the equation of the ellipse with major axis vertical length $$14$$, minor axis length $$6$$, and center $$(-1, 2). $$Express your answer in standard form.

Accepted Answer

$$\frac{(x+1)^2$}{9} + \frac{(y-2)^2$}{49} = 1$$

Question 14

Given the parametric equations $$x = 17 \cos(t)$$, $$y = 17 \sin(t)$$ for $$t \in [0, 2\pi]$$, what is the rectangular equation of the curve?

Accepted Answer

$$x^2$$ + $$y^2 = 289$

Question 15

For the hyperbola $$\frac{x^2$}{25} - y^2$ = 1$$, what are the equations of the asymptotes?

Accepted Answer

$$y = 5x$$, $$y = -5x$$

Question 16

For the hyperbola $$\frac{(x+1)^2$}{36} - \frac{(y-2)^2$}{64} = 1$$, what are the equations of the asymptotes?

Accepted Answer

$$y-2 = \pm \frac{4}{3}(x+1)$$

Question 17

The equation $$y^2 + 4y - x - 3 = 0$ is a parabola. What is its domain and range, and is it a function?

Accepted Answer

Domain: $$[-7, \infty)$$, Range: $$(-\infty, \infty)$$; Not a function

Question 18

Solve the following system using Cramer's Rule: $$\begin{cases} 2x + 3y = 36 \ x - 2y = -17 \end{cases}. $$What are the values of $$x$$ and $$y$$?

Accepted Answer

$$x = 3$$, $$y = 10$$

Graphing Exponential Functions and Identifying Their Properties

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