Graphing square root and cube root

functionsCK-12

7.47.5

Standards

• CCSS.MATH.CONTENT.HSF.IF.C.7Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.• CCSS.MATH.CONTENT.HSF.IF.C.7.B

Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.• CCSS.MATH.CONTENT.HSF.BF.B.3

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Objective

• Graph square root and cube root functions

Example 1

• Graph

This is the parent function.

These graphs will have the form:

• A table of values can be created to give defined points:

• x > 0 here since the square root can not be of a negative number

Example 2

• This is in the square root function form:

• (h,k) is the starting point

• With a table of values:

• The graph is shifted 2 units to the rightand 5 units up.

Example 3

• Graph starts at (-1, 0)• The “a” value controls the width, just like a parabola.• Because it is the inverse of a parabolic function, the “a” value controls

the width of the root function inversely (3 here will make it wider)

• Domain is x > -1, range is y > 0

Example 4

• Starting point is (2, 3)• a = -1, graph is upside down

Practice 1-4

4)

Starting point is(5,1)

Example 5

• Graph

• This is the parent function of

Example 6

• h = 0 and k = 5, there is a shift of 5 units.

Example 7

• (h,k) is (-2,-3), that is the starting point.• a = -1, the graph will be a reflection

• To make the graph more accurate, find a few critical points

Example 8

• (4, 0) is the starting point• a = ½, this will shrink the graph

Practice 5-8

HW

• Khan Academy:• Graphs of square root functions