Q: Which of the following best describes the end behavior of the polynomial $$f(x) = -2x^5$ + 3x^2$ - 7$$?

$$f(x) \to -\infty$$ \, \text{as} \, x \to \infty$

Question 1

Given the linear function passing through the points $$(-2, 5)$$ and $$(4, -1)$$, what is its equation in slope-intercept form?

Accepted Answer

Question 2

Which of the following best describes the end behavior of the polynomial $$f(x) = -2x^5$ + 3x^2$ - 7$$?

Accepted Answer

$$f(x) 	o -\infty$$ \, 	ext{as} \, x 	o \infty$

Question 3

A quadratic function has its vertex at $$(2, -3)$$ and passes through the point $$(4, 5). $$What is its equation in vertex form?

Accepted Answer

$$y = 2(x-2)^2$ - 3$$

Question 4

Which of the following is the correct domain for the function $$f(x) = \dfrac{2x+1}{x^2$-9}$$?

Accepted Answer

$$x 
eq 3, x 
eq -3$$

Question 5

If $$f(x) = \sqrt{x-4}$$, what is the range of $$f(x)$$?

Accepted Answer

$$[0, \infty)$$

Question 6

Which transformation is applied to $$f(x) to $$obtain $$g(x) = 3f(x-2) + 5$$?

Accepted Answer

Shift right 2, stretch vertically by 3, shift up 5

Question 7

Given the absolute value function $$f(x) = |x-3|$$, what is the vertex of its graph?

Accepted Answer

$$(3, 0)$$

Question 8

A rational function has a vertical asymptote at $$x = 2$$ and a horizontal asymptote at $$y = -1. $$Which of the following could be its equation?

Accepted Answer

$$f(x) = \dfrac{3}{x-2} - 1$$

Question 9

Which of the following describes the graph of $$f(x) = -|x|$$ compared to $$f(x) = |x|$$?

Accepted Answer

It is reflected over the $$x-$$axis

Question 10

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

Accepted Answer

$$(x+1)^2$$

Question 11

A quadratic function $$f(x) = ax^2$ + bx + c$$ opens downward and has its vertex at $$(1, 4). $$Which of the following could be its equation?

Accepted Answer

$$f(x) = -2(x-1)^2$ + 4$$

Question 12

Which of the following is the correct equation for a root function that starts at $$(2, 0)$$ and passes through $$(6, 4)$$?

Accepted Answer

$$f(x) = 2\sqrt{x-2}$$

Question 13

Given the polynomial $$f(x) = (x+1)^2$(x-3)$$, what is the multiplicity of the root at $$x = -1$$ and what does it indicate about the graph at this root?

Accepted Answer

Multiplicity 2, graph touches and turns at the axis

Question 14

Which of the following is the correct range for the rational function $$f(x) = \dfrac{1}{x-1} + 2$$?

Accepted Answer

$$y 
eq 2$$

Question 15

If $$f(x) = |x+4|$$, what is the domain and range of $$f(x)$$?

Accepted Answer

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

Question 16

A rational function has a vertical asymptote at $$x = -1$$ and a horizontal asymptote at $$y = 0. $$Which of the following could be its equation?

Accepted Answer

$$f(x) = \dfrac{2}{x+1}$$

Question 17

Which of the following describes the effect of the transformation $$f(x) 	o f(-x) on $$the graph of $$f(x)$$?

Accepted Answer

Reflects the graph over the $$y-$$axis

Question 18

Given $$f(x) = x^2$ and g(x) = 2x + 1$, what is the domain of (f$$ \circ g)(x)$$?

Accepted Answer

$$(-\infty, \infty)$$

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