Unit 8 Review -- 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

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

•  $y=a\sqrt{x-h}+k$  

• If a is negative, the function is reflected

• h controls horizontal movement (always OPPOSITE)

• k controls vertical movement

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