Solving and Graphing Rational Equations

Solve the rational equation: (x + 3) / (x - 2) = 5

• x = 10

• x = 7

• x = -1

• x = 13

Graph the rational function: f(x) = (2x + 1) / (x - 4)

• To graph rational functions, only the numerator needs to be considered.

• Graphing rational functions involves finding the derivative of the function.

• The graph of a rational function always intersects the x-axis at the point where the denominator is zero.

• Graphing rational functions involves finding vertical and horizontal asymptotes, plotting these asymptotes, and analyzing the behavior of the function to sketch the graph.

Identify the vertical asymptote of the function: g(x) = 1 / (x - 1)

• x = -1

• x = 0

• x = 1

• x = 2

Find the horizontal asymptote of the function: h(x) = (3x^2 + 2) / (2x^2 + 1)

• y = 4/3

• y = 3/2

• y = 1/2

• y = 2/3

Solve:

• A

• B

• C

• D

Solve

• A

• B

• C

• D

Solve the equation for x.

• 7

• 6

• 14

• 0

Solve

• A

• B

• C

• D

Solve the rational equation: (2x - 1) / (x + 3) = 3, and check for extraneous solutions

• The solution is x = -3. There are no extraneous solutions.

• The solution is x = 2. There are no extraneous solutions.

• The solution is x = 4. There are no extraneous solutions.

• The solution is x = 3. There are no extraneous solutions.

Identify the vertical asymptote of the function: m(x) = 2 / (x^2 - 4)

• x = 1

• x = -1

• x = 2, x = -2

• x = 3