Square Root Functions
Square Root Functions
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Friday – 2/25/11
Section 7-3, Page 424
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Graphing Square Root Functions
Finding Domains and Ranges
The domain of a square root function is limited to the values of x that
will keep the radicand (under the square root) nonnegative.
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The domain and range of a square root function: f ( x) = 2 x + 6 + 2
1. To find the domain write an inequality
2x + 6 ≥ 0
setting the expression under the radical
x ≥ −3
greater than or equal to 0, then solve it.
2. To find the range evaluate the value found f (−3) = 2(−3) + 6 + 2
in the domain (-3) in the function. This
f (−3) = 2
value is the lower limit of the range.
3. Write the domain and range:
Domain: x ≥ 0
Range: f(x) ≥ 2
Find the domain and range of the function f ( x) = 2 x − 5 − 1
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If a function contains the square root of a variable, it is
called a a square root function. Square root functions
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are a special type of radical function.
The function f(x) = x is a curve that starts at (0, 0) and
continues towards +∞ as x gets larger.
The domain is: x ≥ 0
The range is: f(x) ≥ 0
f ( x) = x
The x-int is: x = 0
The y-int is: y = 0
End behavior:
As x → 0, f(x) → 0 and As x → +∞, f(x) → +∞
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The general form of a square root functions is f ( x) = a x − h + k
The values h and k determine how the graph shifts and the domain
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and range of the function:
h is the opposite of the value under the radical and will shift
the graph right if h is positive and left if h is negative. The
domain is x ≥ h.
k is the value outside the radical and will shift the graph up if k
is positive and down if k is negative. The range is f(x) ≥ k.
The value a changes the size and direction of the graph, and if a is
negative the graph is reflected over the x-axis.
The graph will begin at the point (h, k) and you will need to create a
table of values to create a graph.
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Examples
Graph each square root function, then state the domain and range.
f ( x) = −2 x − 2 + 1
x) =1 01x0 +110
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00 11f 0(010
x
x
f(x)
f(x)
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Assignment #3
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Pg. 427: 4 – 6, 13 – 25, 40, 49 skip 19, 20
Due Tuesday, 3/1/11
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