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?

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

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