Q: Which of the following systems has no solution?

$$\begin{cases} x + y = 2 \\ x + y = 5 \end{cases}$$

Question 1

Which of the following best describes a function?

Accepted Answer

A relation where each input has exactly one output.

Question 2

Given the linear equation $$y = 3x - 5$$, what is the slope and what does it represent in a real-world context?

Accepted Answer

Slope is $$3$$, representing the rate of change of $$y$$ with respect to $$x.$$

Question 3

Which equation represents a line passing through the point $$(2, 4)$$ with a slope of $$-2$$?

Accepted Answer

$$y - 4 = -2(x - 2)$$

Question 4

If $$f(x) = x^2$ + 3x$$ and $$g(x) = 2x - 1$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$(f \circ g)(x) = (2x - 1)^2$ + 3(2x - 1)$$

Question 5

Which of the following is the vertex form of a quadratic function?

Accepted Answer

$$y = a(x - h)^2$ + k$$

Question 6

A company models its profit with $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold. What is the maximum profit?

Accepted Answer

$$P(2) = -2(2)^2$ + 8(2) + 10 = 18$$

Question 7

Which of the following is a possible remainder when dividing $$f(x) = x^3$ - 2x + 5 by$$ $$x - 2$$?

Accepted Answer

$$f(2) = 8 - 4 + 5 = 9$$

Question 8

Which of the following is the correct inverse of $$f(x) = 3x + 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 7}{3}$$

Question 9

A population of bacteria doubles every 3 hours. If the initial population is 500, which function models the population after $$t$$ hours?

Accepted Answer

$$P(t) = 500 \cdot 2$$^{t/3}$$

Question 10

Solve for $$x$$: $$\log_2$(x) = 5$$

Accepted Answer

$$x = 32$$

Question 11

Which of the following systems has no solution?

Accepted Answer

$$\begin{cases} x + y = 2 \ x + y = 5 \end{cases}$$

Question 12

Given the matrix equation $$\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 11 \end{bmatrix}$$, what is the value of $$x$$?

Accepted Answer

$$x = 1$$

Question 13

Which transformation shifts the graph of $$f(x) up by 4 $$units and reflects it across the $$y-$$axis?

Accepted Answer

$$f(-x) + 4$$

Question 14

A rational function has a vertical asymptote at $$x = 3. $$Which of the following could be its equation?

Accepted Answer

$$f(x) = \frac{2x}{x - 3}$$

Question 15

If $$f(x) = x^2$ - 4x + 3$$, what are the zeros of the function?

Accepted Answer

$$x = 1$$ and $$x = 3$$

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