Radical Functions

Unit 8 Review -- Radical Functions

Solving radical equations

• First get the root alone, then get the variable alone

• add/subtract constants

• multiply/divide coefficients

• square/cube both sides

• solve what is left

Fill in the Blanks

Solve the equation, type your answer as a number and nothing else (you won't need to round)

$^3\sqrt{x+5}+6=11$  

Fill in the Blanks

Solve the equation, type your answer as a number and nothing else (you won't need to round it)

$\sqrt{x+3}=14$  

Domain & Range

• Ask yourself: does this function have a starting or stopping point?

• If yes: use the vertex to help you determine domain and range

• If no: it is most likely (-inf, inf)

Multiple Choice

Select the domain of the function

• $$\left(-\infty,\infty\right)$$

• $$\left[-2,\infty\right)$$

• $$\left(-\infty,-2\right]$$

• $$\left[0,\infty\right)$$

Multiple Choice

Select the range of the function

• $$\left(-\infty,\infty\right)$$

• $$\left[-2,\infty\right)$$

• $$\left(-\infty,-2\right]$$

• $$\left[0,\infty\right)$$

Multiple Choice

Select the domain of the function

• $$\left(-\infty,\infty\right)$$

• $$\left[-2,\infty\right)$$

• $$\left[1,\infty\right)$$

• $$\left(-\infty,-2\right]$$

Multiple Choice

Select the range of the function

• $$\left(-\infty,\infty\right)$$

• $$\left[-2,\infty\right)$$

• $$\left[1,\infty\right)$$

• $$\left(-\infty,-2\right]$$

Transformations

Multiple Choice

Which of the following functions matches the graph?

• $$y=\sqrt{3x}$$

• $$y=\sqrt{x}+3$$

• $$y=\sqrt{x+3}$$

• $$y=\sqrt{x-3}$$

Multiple Choice

Which of the following equations matches the graph?

• $$y=\sqrt{x-3}$$

• $$y=\sqrt{x+3}$$

• $$y=\sqrt{x}-3$$

• $$y=\sqrt{x}+3$$

Multiple Select

Given the function

$$f\left(x\right)=\sqrt{x+5}+4$$  , select all of the transformations

• reflection

• left 5

• right 5

• up 4

• down 4

Multiple Select

Given the function

$$g\left(x\right)=\sqrt{x-6}+2$$  select all of the transformations

• reflection

• left 6
  

• right 6

• down 2

• up 2

WoRd PrObLeMs

• Figure out which variable you need to solve for

• Plug in the information you are given

• Desmos is your friend

Multiple Choice

Which variable will we need to solve for in this problem?

• s

• g

• d

Multiple Choice

Which variable is the problem asking you to solve for?

• f

• p