Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice). Patrick Jones

52–55 Solve the given rational equation.

      52.

      53.

      54.

      55.

Polynomial and Rational Inequalities

       56–59 Solve the given polynomial or rational inequality.

      56. x² - 4x - 32 < 0

      57.

      58.

59.

Absolute Value Inequalities

       60–62 Solve the absolute value inequality.

      60.

      61.

      62.

Graphing Common Functions

       63–77 Solve the given question related to graphing common functions.

      63. What is the slope of the line that goes through the points

and

?

      64. What is the equation of the line that has a slope of 4 and goes through the point

?

      65. What is the equation of the line that goes through the points

and

?

      66. Find the equation of the line that goes through the point

and is parallel to the line

.

      67. Find the equation of the line that goes through the point

and is perpendicular to the line that goes through the points

and

.

      68. What is the equation of the graph of

after you stretch it vertically by a factor of 2, shift the graph 3 units to the right, and then shift it 4 units upward?

      69. Find the vertex form of the parabola that passes through the point

and has a vertex at

.

70. Find the vertex form of the parabola that passes through the point

and has a vertex at

.

      71. A parabola has the vertex form

. What is the vertex form of this parabola if it’s shifted 6 units to the right and 2 units down?

      72. What is the equation of the graph of

after you compress the graph horizontally by a factor of 2, reflect it across the y-axis, and shift it down 5 units?

      73. What is the equation of the graph of

after you stretch the graph horizontally by a factor of 5, reflect it across the x-axis, and shift it up 3 units?

      74. Find the equation of the third-degree polynomial that goes through the points

,

,

, and

.

      75. Find the equation of the fourth-degree polynomial that goes through the point

and has the roots –1, 2, and 3, where 3 is a repeated root.

      76. A parabola crosses the x-axis at the points

and

. If the point

is on the parabola, what is the equation of the parabola?

      77. A parabola crosses the x-axis at the points

and

, and the point

is on the parabola. What is the equation of the parabola?

Domain and Range from a Graph

       78–80 Find the domain and range of the function with the given graph.

      78.

      79.

      80.

End Behavior of Polynomials

      81–82 Find the end behavior of the given polynomial. That is, find