2.2 Practice – Domain and Range (Graphs) Answer Key Name: __________________________ Pre‐Calculus For 1‐12, name the basic function shown and write the equation. Try not to look back at your notes if possible.
Greatest Integer Function Exponential Function Square Root Function y
y

y








  



x












x
   

√ Logistic Function y
y


    
  














x
  


Cubic Function Quadratic Function y
y
    
  







  

x
  




x










y


x
    



x
Rational Function 





Sine Function 



y



y
x
x
    


x

y



| | Linear Function 

Logarithm Function 


Cosine Function y

x







x

Absolute Value Function 
For 13‐16, identify the domain intervals where each function is increasing, decreasing, and constant. Use interval notation. 13) y
Inc: Dec: 2, 1
∞, 2
∪ 1,4 ∪ 4, ∞ 14) Inc: 1,4 y
Dec: 3,1 x
Constant: None x
Constant: ∞, 3 ∪ 4, ∞ 15) Inc: 2,1 y
Dec: ∞, 2
∪ 1,5 y
16) Inc: Dec: ∞, 3
3, 1
∪ 2,3 ∪ 1,0
x
x
Constant: 5, ∞ Constant: 0,2 ∪ 3, ∞ For 17‐26, identify the domain and range of each function. Use both interval notation and inequality notation. Domain: Domain: 17) 18) Interval: ∞, ∞ Interval: 1,1 Inequality: all real numbers 1 Inequality: 1
Range: Range: Interval: ∞, 0 Interval: 1,5 Inequality: 0 5
Inequality: 1
Domain: Domain: 20) 
19) 
Interval: 3,
∞
Interval: 0,5 



Inequality: Inequality: 0
3 5 








Range: Range: 

Interval: 1,
∞
Interval: 0, 1, 2, 3, 4 










Inequality: Inequality: 0, 1, 2, 3, 4
1
Domain: Domain: 22) 21) Interval: 5,2
∪
2,4
Interval: 4,4 Inequality: 5
2 4 Inequality: 4
and2
4 Range: Range: Interval: 4, 2 ∪ 1, 3 Interval: 2,2 Inequality: 4
2
2 Inequality: 2
and 1
3
Domain: Domain: 23) 24) Interval:
∞,
∞
Interval: 5, 1 ∪
1,5 Inequality: all real numbers 1
Inequality: 5
Range: 1
5 Interval: 1, ∞ Range: Interval: 4, 2 ∪ 2,4 1 Inequality: 2
Inequality: 4
y





x




y













x













y
y
x
x
y
y







x









x
















y
y








x













x















and 2
25) y
x
Domain: Interval: 4,4 Inequality: 4
Range: Interval: 2,2 Inequality: 2
y
26) 


x
4 








2






4
Domain: Interval: ∞, 1 ∪ 1, ∞ Inequality: 1 Range: Interval: ∞, 1 ∪
1, ∞ 1 Inequality: