GRAPHING RADICAL FUNCTIONS
VOCABULARY
Radical function: A function that can be written in the form 𝑓 𝑥 =
&
𝑥 − ℎ + 𝑘, 𝑤ℎ𝑒𝑟𝑒𝑎 ≠ 0. For even values of n, the domain of a
radical function is the real numbers x > h.
EX: 𝑓 𝑥 = 𝑥 − 2
Square Root Function: a function that can be written in the form
𝑓 𝑥 = 𝑎 𝑥 − ℎ + 𝑘, 𝑤ℎ𝑒𝑟𝑒𝑎 ≠ 0. The domain of a square root
function is all real numbers x > h.
EX: 𝑓 𝑥 = 2 𝑥 − 3 + 1
Families of Radical
Functions
SQUARE ROOT
Parent Function
RADICAL
𝒚= 𝑥
𝑦=
&
𝑥
&
Reflection in x-axis
𝒚=− 𝑥
𝑦=− 𝑥
Stretch: a > 1
Shrink: 0 < a < 1
𝒚=𝒂 𝑥
𝑦=𝑎 𝑥
Translation
Horizontal by h
Vertical by k
𝒚= 𝑥−ℎ+𝑘
&
𝑦=
&
𝑥−ℎ+𝑘
Translating a Square Root Function Vertically
EXAMPLE #1: Graph 𝒚 =
Rewriting a radical function
𝟑
EXAMPLE #10: How can you rewrite 𝒚 = 𝟖𝒙 + 𝟑𝟐 − 𝟐 so you can
graph it using transformations? Describe the graph. Then, sketch
the graph. Check your results with a calculator.
𝑥+2
Domain:
EXAMPLE #2: Graph 𝒚 =
Range:
𝑥−3
Domain:
Range:
Solving a radical equation by graphing
EXAMPLE #7: The population of Corpus Christi, Texas, between 1970
3
and 2005 can be modeled by the function 𝑃(𝑥) = 75000 𝑥 − 1950,
where x represents the year. In what year was the population of
Corpus Christi 275,000?
Translating a Square Root Function Horizontally
EXAMPLE #3: Graph 𝒚 =
𝑥+2
Domain:
EXAMPLE #4: Graph 𝒚 =
Range:
𝑥−3
Domain:
Range:
Graphing a Square Root Function
EXAMPLE #5: Graph 𝒚 = 𝟐 𝑥 + 3 − 1
Graphing a cube root function
EXAMPLE #7: Graph 𝒚 =
C
𝑥−2
Domain:
EXAMPLE #6: Graph 𝒚 = −
Range:
𝟏
𝟐
Domain:
𝑥−1+4
EXAMPLE #8: Graph 𝑦 = 1 −
Range:
13
2
𝑥+3
Domain:
Range:
Domain:
Range: