Q: Write the augmented matrix for the system: $$\begin{cases} 3x + y - 2z = 7 \\ 2y - 4z = 10 \\ -4x + 5z = -9 \end{cases}$$

$$\begin{bmatrix} 3 & 1 & -2 & 7 \\ 0 & 2 & -4 & 10 \\ -4 & 0 & 5 & -9 \end{bmatrix}$$

Q: Given the matrix $$A = \begin{bmatrix} 2 & -1 & 3 \\ 0 & 4 & -5 \end{bmatrix}$$ and $$B = \begin{bmatrix} 0 & 3 & 8 \\ -6 & 1 & 9 \end{bmatrix}$$, find $$A - 2B.$$

$$\begin{bmatrix} 2 & -7 & -13 \\ 12 & 2 & -23 \end{bmatrix}$$

Question 1

Given the graph of $$y = f(x)$$ shown in the first image, what is the domain of $$f in $$interval notation?

Accepted Answer

$$[-10, 7]$$

Question 2

For the function $$f(x) = x^2$ + 6x - 2$$, what are the coordinates of the vertex?

Accepted Answer

$$(-3, -11)$$

Question 3

Given $$f(x) = |x|$$, what is the equation for $$g(x)$$, which is the graph of $$f(x)$$ reflected across the x-axis and stretched horizontally by a factor of 2?

Accepted Answer

$$g(x) = -|\frac{x}{2}|$$

Question 4

Which of the following is a polynomial of degree 3 that crosses the x-axis at $$(2,0)$$ and touches the x-axis at $$(-3,0)$$?

Accepted Answer

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

Question 5

Given the demand equation $$p = -\frac{1}{3}x + 100$$, what is the revenue function $$R(x) in $$terms of $$x$$?

Accepted Answer

$$R(x) = -\frac{1}{3}x^2$ + 100x$$

Question 6

For the function $$f(x) = -1(x-3)(x+1)^2$, what is the multiplicity of the zero at x = -1$ and does the graph touch or cross the x-axis at this point?

Accepted Answer

Multiplicity 2, touches the x-axis

Question 7

What is the end behavior of $$f(x) = -20x$$^{301}$$ + 45x$$^{20}$$ - 456 as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o -\infty$$

Question 8

Given $$f(x) = \frac{(x+5)(x+1)}{(2x+5)(x+1)}$$, what is the equation of the vertical asymptote?

Accepted Answer

$$x = -\frac{5}{2}$$

Question 9

Which regression model is most appropriate for a scatterplot that shows a parabolic pattern?

Accepted Answer

Quadratic

Question 10

Solve the inequality $$\frac{(x-1)^2$(x+2)^3$$}{$$x^2(x-3$$)} \leq 0$. Which of the following intervals is part of the solution?

Accepted Answer

$$(-2, 0)$$

Question 11

What is the domain of the function $$f(x) = \sqrt{x^2$ + 3x + 2}$$?

Accepted Answer

Question 12

Write the augmented matrix for the system: $$\begin{cases} 3x + y - 2z = 7 \ 2y - 4z = 10 \ -4x + 5z = -9 \end{cases}$$

Accepted Answer

$$\begin{bmatrix} 3 & 1 & -2 & 7 \ 0 & 2 & -4 & 10 \ -4 & 0 & 5 & -9 \end{bmatrix}$$

Question 13

Given the matrix $$A = \begin{bmatrix} 2 & -1 & 3 \ 0 & 4 & -5 \end{bmatrix}$$ and $$B = \begin{bmatrix} 0 & 3 & 8 \ -6 & 1 & 9 \end{bmatrix}$$, find $$A - 2B.$$

Accepted Answer

$$\begin{bmatrix} 2 & -7 & -13 \ 12 & 2 & -23 \end{bmatrix}$$

Question 14

Which of the following describes the transformation for $$g(x) = -f(x+2)$$ relative to $$f(x)$$?

Accepted Answer

Reflect across the x-axis and shift left 2 units

Question 15

Given the function $$f(x) = \frac{x^2$ + 6x + 5}{2x^2$ + 7x + 5}$$, what is the equation of the horizontal asymptote?

Accepted Answer

$$y = 0$$

Question 16

For the piecewise function $$f(x) = \begin{cases} -2x-4 & 	ext{if } -4 \leq x \u003c 0 \ 3x & 	ext{if } x \geq 0 \end{cases}$$, what is the value of $$f(0)$$?

Accepted Answer

$$0$$

Question 17

Given the system of equations corresponding to the augmented matrix $$\begin{bmatrix} 4 & 3 & 0 & 19 \ 0 & 5 & -3 & 2 \ 1 & 7 & 6 & 10 \end{bmatrix}$$, what is the equation for the second row?

Accepted Answer

$$0x + 5y - 3z = 2$$

Question 18

If $$h(x) = \frac{1}{2}f(x) - 1$$, which of the following describes the transformation from $$f(x) to$$ $$h(x)$$?

Accepted Answer

Vertical compression by $$\frac{1}{2}$$ and shift down 1

Question 19

Find the $$y-$$intercept of $$f(x) = -1(x-3)(x+1)^2$.

Accepted Answer

$$f(0) = -9$$

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