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U7D9 Review Adding and Graphing Rational Equations May9

Last updated 7 months ago
16 questions
1

Simplify the expression.

1

Simplify the expression.

1

Simplify the expression.

1

Simplify the expression.


1
A = _______
B = _______
C = _______
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A = _______
B = _______
1
A = _______
B = _______
C = _______
1
A = _______
B = _______
C = _______
1
A = _______
B = _______
1
A = _______
B = _______
C = _______
1
A = _______
B = _______
1
A = _______
B = _______
C = _______
1
A = _______
B = _______
C = _______
1
A = _______
B = _______
C = _______
Graphing Rational Functions

Example:
Graph the following rational function and answer the following questions.

Horizontal Asymptote:
Compare the degree of the numerator (n) and the degree of the denominator (d).
If n < d, then H.A. at y = 0
If n = d, then H.A. at y = (lead coefficient/lead coefficient)
If n > d, then there is a slant asymptote

n = d
so the H.A. for f(x) is at y = 1.

Vertical Asymptote:
Occur when a number makes the denominator equal 0. These numbers would make the fraction undefined.

x + 2 = 0 when x = -2
so the V.A. for f(x) is at x = -2.

X-Intercept:
Any number that make the numerator equal 0 is an x-intercept.

x - 6 = 0, when x = 6
so x-intercept at (6,0)

Y-Intercept:
Y-intercepts occur at the result from plugging zero in for x.

so y-intercept at (0,-3)


Domain - All the possible x-values that can be used in the function.




Range - All possible results from the inputs.




Find the DOMAIN and RANGE for:

Solution:
Begin with the graph for the function.
In this graph, any number could be x (domain), except -2.
-2 makes the denominator zero, so it is not permitted.

Domain: All real numbers except -2
or


For the range, this graph shows our results could be any value except 1.
Range: All real numbers except 1
or
1
Graph the following rational function and answer the following questions.

Horizontal Asymptote: _______
Vertical Asymptote: _______
X-intercept: _______
Y-intercept: _______
Domain: _______
Range: _______
1
Graph the following rational function and answer the following questions.

Horizontal Asymptote: _______
Vertical Asymptote: _______
X-intercept: _______
Y-intercept: _______
Domain: _______
Range: _______