Section 7.9:
Objectives:
Square Root Functions and Inequalities
Graph and analyze square root functions.
Graph square root inequalities.
Square Root Function:
a function that contains a square root; resembles a curve (not a line, parabola, etc.)
Graph a Square Root Function
EX 1: Graph y =
3x  4
*Since the function cannot be negative,
we must first find the minimum value of x.
This is the point where we will start graphing.
To do this, we say the value under the radical
is greater than or equal to zero.
3x + 4 ≥ 0
3x ≥ -4
x ≥ 4
3
*Now that we know the minimum value of x,
we plug in values that are greater than this
number to find other points.
EXTRA EXAMPLES
Graph y =
2x  4
Graph y =
x 1
Graph a Square Root Inequality
*All rules that we learned when graphing linear inequalities and quadratic inequalities still apply.
* If the symbol is < or >, the line is dotted.
* If the symbol is ≤ or ≥, the line is dotted.
* If the function is > or ≥, shade above the graph
* If the function is < or ≤, shade below the graph.
EX 2: Graph y <
2x  6
EX 3: Graph y ≥
x 1

We start these problems off the same way as
when graphing a square root function (EX 1).

We start these problems off the same way as
when graphing a square root function (EX 1).

Since the inequality symbol is <, that means
the line is dotted and we shade under the
curve.

Since the inequality symbol is ≥, that means
the line is solid and we shade above the curve.
EXTRA EXAMPLE
Graph y ≤
x  4 1