Algebra 2 Pre-AP Unit 5A DA Square & Cube Root & Rational

The cube root function $y=x^{\frac{1}{3}}$   is changed into  $y=-\left(x-4\right)^{\frac{1}{3}}$ . Which best describes the change to the graph of the original function? (TEKS A2.6A-S)

• The original graph is shifted 4 units to the left and then reflected over the x-axis.

• The original graph is reflected over the y-axis and then shifted 4 units to the left.

• The original graph is shifted 4 units to the right and then reflected over the y-axis.

• The original graph is reflected over the x-axis and then shifted 4 units to the right.

Tags

CCSS.HSF-IF.C.7B

Which statement represents the  $f^{-1}\left(x\right)\ of\ f\left(x\right)=x^3-7$ ? (TEKS A2.2B-S)

•  $f^{-1}\left(x\right)=7-x^3$  

•  $f^{-1}\left(x\right)=\frac{1}{x^3-7}$  

•  $f^{-1}\left(x\right)=x^3+7$  

•  $f^{-1}\left(x\right)=\left(x+7\right)^{\frac{1}{3}}$  

Tags

CCSS.HSF-BF.B.4A

Solve each equation. Identify the one with no extraneous solution. (TEKS A2.4G-S)

• $\sqrt{x+4}+7=5$

• $\left(x-3\right)^{\frac{1}{2}}=6$

• $x+\sqrt{x+2}=4$

• $-\sqrt{x-1}=1$

Tags

CCSS.HSA.REI.A.2

Which function is represented by this graph? (TEKS A2.4C-R)

• $y=\sqrt{x-1}-3$

• $y=\sqrt{x-3}-1$

• $y=\sqrt{x+1}-3$

• $y=\sqrt{x-3}+1$

Tags

CCSS.HSF-IF.C.7B

 Which expression is equivalent to  $\sqrt{8x^8y^3z^{32}}$  in lowest terms? (TEKS A2.7G-S) 

•  $2x^4yz^{16}\sqrt{2y}$  

•  $2x^6yz^{30}\sqrt{2}$  

•  $4x^4yz^{16}\sqrt{y}$  

•  $4x^6yz^{30}$  

Which inequality describes the domain of the equation  $y=\sqrt{2x-7}$  ? (TEKS A2.7I-S)

•  $x\ge7$  

•  $x\ge\frac{7}{2}$  

•  $x\le7$  

•  $x\le\frac{7}{2}$  

Which describes the graph of the function  $y=\sqrt{x+2}-5$  ? (TEKS A2.4C-R)

•  $y=\sqrt{x}$  shifted 2 units up and 5 units right.

•  $y=\sqrt{x}$  shifted 5 units down and 2 units right.

•  $y=\sqrt{x}$   shifted 2 units up and 5 units left.

•  $y=\sqrt{x}$   shifted 5 units down and 2 units left.

Tags

CCSS.HSF-IF.C.7B

Which function has an inverse that is also a function if and only if the domain is restricted to  $x\le5\ or\ x\ge5$  ? (TEKS A2.2C-R)

•  $f\left(x\right)=\sqrt{2x+4}$  

•  $f\left(x\right)=\left(x-5\right)^2+3$  

•  $f\left(x\right)=4x^2+20x+25$  

•  $f\left(x\right)=\left(2x+3\right)^{\frac{1}{3}}$  

Tags

CCSS.HSF-BF.B.4D

What is the value of x in the equation  $\left(x+28\right)^{\frac{1}{3}}=4$ ? (TEKS A2.6B-S) 

• -16

• -12

• 24

• 36

The table includes values of a square root function rounded to the nearest hundredth. Which function is represented by the table? (TEKS A2.4E-S)

•  $y=\frac{\sqrt{x}}{4}$  

•  $y=4\sqrt{x}$  

•  $y=\sqrt{\frac{x}{4}}$  

•  $y=\sqrt{4x}$  

Tags

CCSS.HSF.LE.A.2