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CATEGORY 3 - A.6(E)The student is expected to determine the intercepts of the graph of linear functions an zeros of linear functions from graphs, tables, and algebraic representations.SUPPORTING STANDARD
KEY TERMSX-INTERCEPT – The x – coordinate where the graph crosses the x – axis.
Y-INTERCEPT – The y – coordinate where the graph crosses the y – axis.
ZERO OF A LINEAR FUNCTION – The x-value that makes the function equal zero.
INTERCEPTS & ZEROS
x - intercept
zero
y - intercept
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Example 1: What are the x – and y – intercepts of the function graphed below?
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x–intercept (-3, 0)
y-intercept(0, -6)
Example 2: What is the x-intercept of the equations -3y = 8 – 2x?To find the x-intercept let y = 0. -3(0) = 8 – 2x Solve for x. 0 = 8 – 2x -8 = -2x 4 = x
The x – intercept is (4, 0)
subtract 8 from both sidesdivide both sides by -2
substitute 0 for y
Example 3: What is the y-intercept of the equations -3y = 8 – 2x?To find the y-intercept let x = 0. -3y = 8 – 2(0) Solve for y. The y – intercept is (0, - )
substitute 0 for x
-3y = 8 y = -
divide both sides by -3
Example 4: What is the zero of the linear function graphed below?
When looking for a zero of a linear function you are actually looking for the x-intercept.
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(0,6)
(2,-6)
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f(x)
x = 1
The zero of the function is 1.
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