Quiz about Chapter 6 Review Algebra 2

Question 1

Simplify. Assume that all variables are positive.

$$\sqrt[]{12x^7}$$

Accepted Answer

$$2x^3\ \sqrt[]{3x}$$

Answer

$$2\ \sqrt[]{3x^7}$$

Answer

$$3\ \sqrt[]{2x^7}$$

Answer

$$2x^6\ \sqrt[]{3x}$$

Answer

$$3x^6\ \sqrt[]{2x}$$

Question 2

Divide and simplify. Assume that all variables are positive.

$$\frac{\sqrt[]{140x^8y^5}}{\sqrt[]{7x^2y^2}}$$

Accepted Answer

$$2x^3y\ \sqrt[]{5y}$$

Answer

$$5xy\ \sqrt[]{2xy}$$

Answer

$$2x^3\ \sqrt[]{5y^2}$$

Answer

$$\sqrt[]{20x^2y^3}$$

Question 3

Simplify by combining like radicals.

$$8\ \sqrt[]{10}+\ 4\ \sqrt[]{10}$$

Accepted Answer

$$12\ \sqrt[]{10}$$

Answer

$$12\ \sqrt[]{20}$$

Answer

$$120$$

Answer

$$12\ \sqrt[]{100}$$

Question 4

Simplify

$$\sqrt[]{28}+\ \sqrt[]{63}$$

Accepted Answer

$$5\ \sqrt[]{7}$$

Answer

$$\sqrt[]{91}$$

Answer

$$6\ \sqrt[]{7}$$

Answer

$$5\ \sqrt[]{14}$$

Question 5

Write the expression shown below in radical form.

$$y^{\frac{1}{5}}$$

Accepted Answer

$$\sqrt[5]{y}$$

Answer

$$\sqrt[1]{y^5}$$

Question 6

Convert the expression from exponential form to radical form.

$$x^{\frac{3}{5}}$$

Accepted Answer

$$\sqrt[5]{x^3}$$

Answer

$$\sqrt[3]{x^5}$$

Question 7

Let $$f\left(x\right)=x+8$$ and $$g\left(x\right)=4x^2$$

Perform the function operation.

(f+g)(x)

Accepted Answer

$$4x^2+x+8$$

Answer

$$\left(x+8\right)+\left(4x^2\right)$$

Answer

$$4x^3+32x^2$$

Answer

$$4x^3+8$$

Question 8

What is the domain of $$4x^2+x+8$$ ?

Accepted Answer

The domain of f+g is the set of all real numbers.

Answer

The domain of f+g is the set of all real numbers except x+0.

Answer

The domain of f+g is the set of all $$x\le0.$$

Answer

The domain of f+g is the set of all $$x\ge0.$$

Question 9

Let $$f\left(x\right)=3x^2+7x-20$$ and $$g\left(x\right)=x+4$$ . Perform the function operation.

$$\left(f\cdot g\right)\left(x\right)$$

Accepted Answer

$$3x^3+19x^2+8x-80$$

Answer

$$3x^3+12x^2+7x^2+28x-20x-80$$

Answer

$$3x^2+8x-16$$

Answer

$$3x^3+27x^2+28x-80$$

Question 10

What is the domain of $$3x^3+19x^2+8x-80$$ ?

Accepted Answer

The domain of f*g is the set of all real numbers.

Answer

The domain of f*g is the set of all $$x\le0.$$

Answer

The domain of f*g is the set of all real numbers except x=0.

Answer

The domain of f*g is the set of all $$x\ge0.$$

Question 11

What is the domain of 4x+7?

Accepted Answer

The domain of f/g is the set of all real numbers except x=-3.

Answer

The domain of f/g is the set of all real numbers.

Answer

The domain of f/g is the set of all x>-3.

Answer

The domain of f/g is the set of all x<-3.

Question 12

Find the inverse of the function.

$$f\left(x\right)=3x-1$$

Accepted Answer

$$\frac{x+1}{3}$$

Answer

$$3x+3$$

Answer

$$3y-1$$

Answer

$$\frac{x-1}{3}$$

Question 13

Is $$\frac{x+1}{3}$$ a function?

Accepted Answer

Yes

Answer

No

Question 14

Find the inverse of the relation shown.

Accepted Answer

Question 15

Find the inverse of the function.

$$y=2x^2-4$$

Accepted Answer

$$y=\ \pm\ \sqrt[]{\frac{x+4}{2}}$$

Answer

$$y=2\ \sqrt[]{x+4}$$

Answer

$$y=\ \sqrt[]{\frac{x-4}{2}}$$

Answer

$$y=\ \pm\ \frac{\sqrt[]{x-4}}{2}$$

Question 16

Is $$y=\ \pm\ \sqrt[]{\frac{x+4}{2}}$$ a function?

Accepted Answer

No

Answer

Yes

Question 17

Sketch the graph of each function.

Accepted Answer

Option C is correct

Answer

A.

Answer

B.

Answer

D.

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