Solving and Graphing Rational Equations

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

• x = 10

• x = 7

• x = -1

• x = 13

Tags

CCSS.HSA.REI.A.2

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.

Tags

CCSS.HSF-IF.C.7D

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

• x = -1

• x = 0

• x = 1

• x = 2

Tags

CCSS.HSF-IF.C.7D

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

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSA.REI.A.2

Solve the rational equation: (x^2 - 4) / (x - 2) = 0

• x = 0

• x = 2

• x = 4

• x = -2

Tags

CCSS.HSA.REI.A.2

Graph the rational function: k(x) = (x^2 - 1) / (x + 1)

• Graph the rational function: k(x) = (x^2 + 1) / (x + 1)

• Graph the rational function: k(x) = (x^2 + 1) / (x - 1)

• The explanation provides the steps to graph the rational function k(x) = (x^2 - 1) / (x + 1) correctly.

• Graph the rational function: k(x) = (x^2 - 1) / (x - 1)

Tags

CCSS.HSF-IF.C.7D

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

• x = 1

• x = -1

• x = 2, x = -2

• x = 3

Tags

CCSS.HSF-IF.C.7D

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

• y = 4/3

• y = 1/2

• y = 3/2

• y = 2/3

Tags

CCSS.HSF-IF.C.7D

Solve the rational equation: (3x + 2) / (x - 1) = 4, and check for extraneous solutions

• x = 2

• x = -3

• x = 6

• x = 0

Tags

CCSS.HSA.REI.A.2