$$y = \begin{cases} -3x + 2,\ -1 \u003c x \u003c 1 \\ 0.5x + 4,\ 1 \leq x \leq 3 \end{cases}$$

Question 1

Given the function $$g(x) = -x + 5$$, what is the domain and range of the function?

Accepted Answer

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

Question 2

Which piecewise formula best describes the graph shown in the first image?

Accepted Answer

$$y = \begin{cases} -3x + 2,\ -1 \u003c x \u003c 1 \ 0.5x + 4,\ 1 \leq x \leq 3 \end{cases}$$

Question 3

For the function $$f(x) = \frac{5x^2$ - 9}{x - 3}$$, what are the equations of all its possible asymptotes?

Accepted Answer

None

Question 4

Given $$f(x) = -5 + 7x$$, which of the following is the correct inverse function and its graph?

Accepted Answer

Inverse: $$f^{-1}(x$$) = \frac{1}{7}x - \frac{5}{7}$$, Graph: Image 2

Question 5

Is the equation $$\frac{\cos A}{1 + \sin A} = \frac{1 - \sin A}{\cos A} a $$trigonometric identity?

Accepted Answer

Not an identity

Question 6

Which table correctly shows the values of trigonometric functions for $$	heta = \frac{\pi}{3}, \frac{5\pi}{6}, \frac{4\pi}{3}$$?

Accepted Answer

Image 6

Question 7

If $$h(x) is a $$function, which graph represents $$h(x + 3)$$?

Accepted Answer

Image 10

Question 8

Which pair of $$u(x)$$ and $$v(x) is $$correct for $$u(v(x)) = (x^3$ - 5)^4$?

Accepted Answer

$$u(x) = x^4$, v(x$$) = $$x^3 - 5$

Question 9

Simplify the expression $$(\frac{10}{5})^3$.

Accepted Answer

2

Question 10

A species of fish doubles its population every 24 hours. If the initial population is 200, what is the population after 3 days?

Accepted Answer

3200

Question 11

Given $$\log_c a = 0.45$$ and $$\log_c b = 0.65$$, find $$\log_c \left(\frac{a}{b}\right).$$

Accepted Answer

$$-0.20$$

Question 12

Identify the intervals where the function $$h(x) = |x + 4| is $$one-to-one and thus has an inverse.

Accepted Answer

$$(-\infty, -4]$$ and $$[4, \infty)$$

Question 13

Which graph best represents the function $$f(x) = \sin 4x + \cos 4x$$?

Accepted Answer

Image 5

Question 14

Which of the following is equivalent to $$\csc$$^{-1}$$(y)$$ for $$y 
eq 0$$?

Accepted Answer

$$\sin$$^{-1}$$(\frac{1}{y})$$

Question 15

Prove the limit statement $$\lim_{x 	o 2}(7 - x) = 5. $$Which choice for $$\delta (in $$terms of $$\varepsilon) $$correctly proves this limit?

Accepted Answer

$$\delta = \varepsilon$$

Question 16

Evaluate the limit $$\lim_{x 	o -\infty} 11e^x \cos x.$$

Accepted Answer

0

Question 17

Which function is continuous on the interval $$(0, 15)$$?

Accepted Answer

Image 14

Step-by-Step Guidance for Calculus Midterm Study Prep (Part 1)

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