Q: Which of the following describes the end behavior of the polynomial $$f(x) = -3x^4$ + 2x^2$ - 7$$?

As $$x \to \infty$$, $$f(x) \to -\infty$$; as $$x \to -\infty$$, $$f(x) \to -\infty$$

Question 1

Given the parent function $$f(x) = x^2$, which transformation results in the graph of g(x$$) = $$(x-3)^2 + 2$?

Accepted Answer

Shift right 3 units and up 2 units

Question 2

What is the domain of the function $$f(x) = \dfrac{1}{x^2$ - 4}$$?

Accepted Answer

$$(-\infty, -2) \cup (-2, 2) \cup (2, \infty)$$

Question 3

Given the quadratic function $$f(x) = 2(x-1)^2$ - 5$$, what are the coordinates of its vertex?

Accepted Answer

$$(1, -5)$$

Question 4

Which of the following is the correct interval notation for the domain of $$f(x) = \sqrt{x-7}$$?

Accepted Answer

$$[7, \infty)$$

Question 5

A company models its profit with the quadratic function $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold. What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Question 6

Which of the following describes the end behavior of the polynomial $$f(x) = -3x^4$ + 2x^2$ - 7$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o -\infty$$; as $$x 	o -\infty$$, $$f(x) 	o -\infty$$

Question 7

Given the linear equation $$y = -2x + 5$$, what are the slope and y-intercept?

Accepted Answer

Slope: $$-2$$, y-intercept: $$5$$

Question 8

Which of the following is the equation of a line passing through $$(2, 3)$$ with a slope of $$4 in $$point-slope form?

Accepted Answer

$$y - 3 = 4(x - 2)$$

Question 9

Given the quadratic function $$f(x) = x^2$ - 6x + 8$$, what are its x-intercepts?

Accepted Answer

$$x = 2$$ and $$x = 4$$

Question 10

Which transformation is applied to the parent function $$f(x) = e^x to $$obtain $$g(x) = e$$^{x-2}$$ + 5$$?

Accepted Answer

Shift right 2 units and up 5 units

Question 11

A population of bacteria is modeled by $$P(t) = 500 \cdot 2^t. $$What is the horizontal asymptote of this function?

Accepted Answer

$$y = 0$$

Question 12

Given the polynomial $$f(x) = (x-1)^2$(x+3)$$, what is the multiplicity of the zero at $$x = 1$$ and how does the graph behave at this zero?

Accepted Answer

Multiplicity 2; the graph touches and turns at $$x = 1$$

Question 13

Which of the following is the correct factored form of $$f(x) = x^2$ - 9$$?

Accepted Answer

$$(x - 3)(x + 3)$$

Question 14

If $$f(x) = \log(x-4)$$, what is the domain of $$f$$?

Accepted Answer

$$(4, \infty)$$

Question 15

A quadratic function models the height $$h (in $$meters) of a ball thrown upward as $$h(t) = -4.9t^2$ + 20t + 1.5. $$What is the maximum height reached by the ball?

Accepted Answer

$$21.95$$ meters

Question 16

Given the function $$f(x) = \dfrac{x^2$ - 1}{x - 1}$$, what is the domain of $$f$$?

Accepted Answer

$$(-\infty, 1) \cup (1, \infty)$$

Question 17

Which of the following is the correct vertex form of the quadratic $$f(x) = x^2$ + 6x + 5$$?

Accepted Answer

$$f(x) = (x + 3)^2$ - 4$$

Question 18

Which of the following is the correct equation for a line with slope $$-\dfrac{1}{2}$$ and y-intercept $$4$$?

Accepted Answer

$$y = -\dfrac{1}{2}x + 4$$

Question 19

Given the exponential function $$f(x) = 3 \cdot 2$$^{x-1}$$, which transformation is applied to the parent function g(x) = 2^x$?

Accepted Answer

Shift right 1 unit and vertical stretch by 3

College Algebra Study Guide: Transformations, Domains, and Graphs of Functions

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