Absolute Value Functions

 $\ h(x)=2∣x−6∣+2$ 

Describe the transformations from the graph of f(x) = ∣ x ∣ to the graph of the given function.

Separate your answer with a comma

 $n(x)=-\frac{1}{2}∣x+3∣$  

Describe the transformations from the graph of f(x) = ∣ x ∣ to the graph of the given function.

Separate your answer with a comma

 $p(x)=-2∣x∣$  

Graph the function (use Desmos or calculator). Compare the graph to the graph of f(x) = ∣ x ∣

 $\left|\frac{27}{-3}\right|$  simplify the expression

• -9

• 9

• no solution
  

• -9 , 9
  

 $∣2c+8∣=∣10c∣$  

Solve the equation. Check your solutions.

•  $c=-\frac{2}{3},\ c=-1$  

•  $c=\frac{2}{3},\ c=1$  

•  $c=\frac{2}{3},\ c=-1$  

•  $c=-\frac{2}{3},\ c=1$  

 $∣3h+1∣=7h$  

Solve the equation. Check your solutions.

•  $h=\frac{1}{4}$  

•  $h=-\frac{1}{10}$  

•  $h=-\frac{1}{10},\ h=\frac{1}{4}$  

•  $h=-\frac{1}{4}$  

 $∣4b−5∣=19$  

Solve the equation

•  $b=3.5,\ b=6$  
  

•  $\ No\ solution$ 
  

•  $b=3.5,\ b=-6$  

•  $b=−3.5,\ b=6$  

 $∣m+3∣=-7$  

Solve the equation

•  $No\ solution$  

•  $m=−10,\ m=4$  

•  $m=10,m=4$  

•  $All\ real\ numbers$  

 $∣5p+2∣<−4$  

Solve the inequality

•  $p=-\frac{6}{5},\ p=\frac{2}{5}$  

•  $p=\frac{2}{5}$  

•  $All\ real\ numbers$  

•  $No\ solution$  

 $−3∣2−4u∣+5<−13$  

Solve the inequalities

•  $No\ solution$  

•  $u>2\ or\ u<−1$  

•  $u>2\ or\ u<−1$  

•  $All\ real\ numbers$