Which of the following best describes how the function $$y=\frac{2}{x+4}-6$$ has been transformed from the parent function $$y=\frac{1}{x}$$ ?

The parent function has been dilated vertically by a factor of 2 and then translated left 4 units and down 6 units.

The parent function has been dilated vertically by a factor of 2.5 and then translated right 4 units and down 6 units.

The parent function has been dilated vertically by a factor of -2 and then translated left 4 units and down 3 units.

The parent function has been dilated vertically by a factor of 2 and then translated right 4 units and down 6 units.

What are the asymptotes for the following function? $$f\left(x\right)=\frac{\left(x+4\right)\left(x-5\right)}{\left(x-5\right)\left(x-3\right)}$$

Horizontal Asymptote: $$y=1$$ Vertical Asymptote: $$x=3$$

Horizontal Asymptote: $$y=1$$ Vertical Asymptote: $$x=-3$$

Horizontal Asymptote: $$y=-3$$ Vertical Asymptote: $$x=1$$

Horizontal Asymptote: $$y=3$$ Vertical Asymptote: $$x=1$$

The first year Eleanor organized a fund-raising event, she invited 30 people. For each of the next 5 years, she invited double the number of people she had invited the previous year. If $$f\left(n\right)$$ is the number of people invited to the fund-raiser $$n$$ years after Eleanor began organizing the event, which of the following statements best describes the function f?

The function f is an increasing exponential function.

The function f is a decreasing linear function.

The function f is an increasing linear function.

The function f is a decreasing exponential function.

Describe the domain, range and asymptote for the function: $$y=\log_2x$$

Domain: $$x>0$$ , Range: all reals, Asymptote: $$x=0$$

Domain: all reals, Range: $$y>0$$ , Asymptote: $$y=0$$

Domain: all reals, Range: $$y\ge0$$ , Asymptote: None

Domain: $$x\ge0$$ , Range: all reals, Asymptote: None

Which of the following best describes how the function $$y=\log_4\left(x-2\right)+3$$ has been transformed from the parent function $$y=\log_4x$$ ?

The parent function has been translated right 2 units and up 3 units.

The parent function has been translated left 2 units and down 3 units.

The parent function has been translated left 2 units and up 3 units.

The parent function has been translated right 2 units and down 3 units.

What is the correct set-up to find the missing side length?

D. $$\frac{x}{\sin 19} = \frac{16}{\sin 52}$$

A. $$\frac{x}{\sin 109} = \frac{16}{\sin 52}$$

B. $$\frac{x}{\sin 19} = \frac{52}{\sin 16}$$

C. $$\frac{x}{\sin 109} = \frac{52}{\sin 16}$$

Which of the following best features of the graph created from the function below? $$y=8\cos\left(x+\frac{\pi}{2}\right)-3$$

Midline $$y=-3$$ , Amplitude $$a=8$$ , Range $$\left[-11,\ 5\right]$$

Midline $$y=-3$$ , Amplitude $$a=8$$ , Range $$\left[-11,\ 8\right]$$

Midline $$y=3$$ , Amplitude $$a=-3$$ , Range $$\left[-11,\ 8\right]$$

Midline $$y=3$$ , Amplitude $$a=-3$$ , Range $$\left[-11,\ 5\right]$$

Algebra 2B Final Exam

Authored by Erin Leugs

Mathematics

11th Grade

CCSS covered

Used 3+ times

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50 questions

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MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Use the finite differences method to determine if the data set can be modeled with a first, second or third degree polynomial.

first degree polynomial

second degree polynomial

third degree polynomial

cannot be determined using finite differences

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Write an equation in factored form for a polynomial function with real coefficients and zeros at $x=4$ , $x=2$ , and $x=-3$ . Assume the leading coefficient is 1.

$y=\left(x-4\right)\left(x-2\right)\left(x-3\right)$

$y=\left(x-4\right)\left(x+2\right)\left(x-3\right)$

$y=\left(x+4\right)\left(x+2\right)\left(x-3\right)$

$y=\left(x-4\right)\left(x-2\right)\left(x+3\right)$

Tags

CCSS.HSA.APR.B.3

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Write the equation of the graph in factored form.

$y=-\frac{1}{4}(x+4)(x+2)(x-2)^2$

$y=-\frac{1}{4}(x+4)(x+2)(x-2)$

$y=(x+8)(x-0)$

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

Tags

CCSS.HSA.APR.B.3

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

What is the lowest possible degree of the polynomial graphed?

$5$

$4$

$3$

$2$

Tags

CCSS.HSA.APR.B.3

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

At what zero is there a multiplicity of 2?

$-1$

$-4$

$1$

$2$

Tags

CCSS.HSF-IF.C.7C

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Describe the long-run behavior for $17x^4 + 543x^2 - 75$ .

As x decreases, y increases. As x increases, y increases.

As x decreases, y increases. As x increases, y decreases.

As x decreases, y decreases. As x increases, y decreases.

As x decreases, y decreases. As x increases, y increases.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Which of the following is a zero when $x^3 + 2x^2 - 5x - 6$ is divided by $x + 1$ ?

$\left(x+3\right)$

$\left(x+2\right)$

$\left(x-3\right)$

$\left(x-1\right)$

Tags

CCSS.HSA.APR.B.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Which of the following is NOT a root of the following polynomial function?
$f\left(x\right)=x^4-27x^2-14x+120$

$-4$

$-3$

$-2$

$5$

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

What is the a-value (leading coefficient) given the following information:
zeros: $x=-1$ (multiplicity of 2), $x=1$ , and $x=6$
y-intercept: $\left(0,\ 2\right)$

$3$

$-3$

$-\frac{1}{3}$

$\frac{1}{3}$

10.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Which of the following functions has this end behavior?
Left end behavior: As x decreases, y increases
Right end behavior: As x increases, y decreases

$f(x) = 2x^3 + 3x^2 + 4x - 9$

$f(x) = -2x^3 + 3x^2 + 4x - 9$

$f\left(x\right)=2x^2+4x-9$

$f(x) = -2x^2 + 4x - 9$

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Algebra 2B Final Exam

Use the finite differences method to determine if the data set can be modeled with a first, second or third degree polynomial.

Write an equation in factored form for a polynomial function with real coefficients and zeros at x=4x=4x=4 , x=2x=2x=2 , and x=−3x=-3x=−3 . Assume the leading coefficient is 1.

Write the equation of the graph in factored form.

What is the lowest possible degree of the polynomial graphed?

At what zero is there a multiplicity of 2?

Describe the long-run behavior for 17x4+543x2−7517x^4 + 543x^2 - 7517x4+543x2−75 .

Which of the following is a zero when x3+2x2−5x−6x^3 + 2x^2 - 5x - 6x3+2x2−5x−6 is divided by x+1x + 1x+1 ?

Which of the following is NOT a root of the following polynomial function? f(x)=x4−27x2−14x+120f\left(x\right)=x^4-27x^2-14x+120f(x)=x4−27x2−14x+120

What is the a-value (leading coefficient) given the following information:zeros: x=−1x=-1x=−1 (multiplicity of 2), x=1x=1x=1 , and x=6x=6x=6 y-intercept: (0, 2)\left(0,\ 2\right)(0, 2)

Which of the following functions has this end behavior?Left end behavior: As x decreases, y increasesRight end behavior: As x increases, y decreases

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Discover more resources for Mathematics

Write an equation in factored form for a polynomial function with real coefficients and zeros at $x=4$ , $x=2$ , and $x=-3$ . Assume the leading coefficient is 1.

Describe the long-run behavior for $17x^4 + 543x^2 - 75$ .

Which of the following is a zero when $x^3 + 2x^2 - 5x - 6$ is divided by $x + 1$ ?

Which of the following is NOT a root of the following polynomial function?
$f\left(x\right)=x^4-27x^2-14x+120$

What is the a-value (leading coefficient) given the following information:
zeros: $x=-1$ (multiplicity of 2), $x=1$ , and $x=6$
y-intercept: $\left(0,\ 2\right)$

Which of the following functions has this end behavior?
Left end behavior: As x decreases, y increases
Right end behavior: As x increases, y decreases