Graphs of Functions and Equations Worksheet

**Page 1**

1.

Find the $x$ and $y$-intercepts of the graph of the equation.

$y$ = $x$^{3} - 8

a. | $x$-intercept: (0, 0); $y$-intercept: (2, - 8) | ||

b. | $x$-intercept: (0, 2); $y$-intercept: (- 8, 0) | ||

c. | $x$-intercept: (2$\sqrt{2}$, 0); $y$-intercept: (0, 8) | ||

d. | $x$-intercept: (2, 0); $y$-intercept: (0, - 8) | ||

e. | $x$-intercept: ($\sqrt[8]{3}$, 0); $y$-intercept: (0, 8) |

[Original Equation.]

Make a table of values of (

^{3} - 8 | ( | |

- 1 | - 9 | (- 1, - 9) |

0 | - 8 | (0, - 8) |

1 | - 7 | (1, - 7) |

2 | 0 | (2, 0) |

3 | 19 | (3, 19) |

Draw the graph by plotting the points and join them with a smooth curve.

The graph crosses the

So, the

Correct answer : (4)

2.

Identify the basic tangent function from the graphs.

a. | Graph 5 | ||

b. | Graph 1 | ||

c. | Graph 2 | ||

d. | Graph 3 | ||

e. | Graph 4 |

Graph 4 represents the tangent function.

Correct answer : (5)

3.

Sketch the graph of the equation $y$ = $\sqrt{x+9}$. Identify the $y$-intercept.

a. | Graph 1; (- 10, 0) | ||

b. | Graph 2; (0, 3) | ||

c. | Graph 4; (3, 0) | ||

d. | Graph 5; (0, - 3) | ||

e. | Graph 3; (0, 10) |

[Original Equation.]

Make a table of values of

( | ||

- 9 | 0 | (- 9, 0) |

- 6 | 1.7 | (- 6, 1.7) |

- 3 | 2.4 | (- 3, 2.4) |

0 | 3 | (0, 3) |

3 | 3.5 | (3, 3.5) |

6 | 3.9 | (6, 3.9) |

Plot the points obtained from the table, which matches with Graph 2.

The

Correct answer : (2)

4.

Identify the basic secant function from the graphs.

a. | Graph 3 | ||

b. | Graph 4 | ||

c. | Graph 1 | ||

d. | Graph 2 | ||

e. | Graph 5 |

Graph 5 represents the secant function.

Correct answer : (5)

5.

Find the $x$-intercept(s) of the graph as shown.

a. | (1, 1) | ||

b. | (0, 2) | ||

c. | (2, 2) | ||

d. | does not exist | ||

e. | (0, 0) |

So, the

Correct answer : (5)

6.

Identify the basic cube root function from the graphs.

a. | Graph 3 | ||

b. | Graph 4 | ||

c. | Graph 5 | ||

d. | Graph 1 | ||

e. | Graph 2 |

Graph 3 represents the cube root function.

Correct answer : (1)

7.

Identify the basic exponential function from the graphs.

a. | Graph 2 | ||

b. | Graph 5 | ||

c. | Graph 3 | ||

d. | Graph 1 | ||

e. | Graph 4 |

Graph 1 represents the exponential function.

Correct answer : (4)

8.

Identify the basic logarithmic function from the graphs.

a. | Graph 5 | ||

b. | Graph 3 | ||

c. | Graph 1 | ||

d. | Graph 2 | ||

e. | Graph 4 |

Graph 2 represents the logarithmic function.

Correct answer : (4)

9.

Identify the constant function from the graphs.

a. | Graph 5 | ||

b. | Graph 4 | ||

c. | Graph 1 | ||

d. | Graph 2 | ||

e. | Graph 3 |

Graph 3 represents the constant function.

Correct answer : (5)

10.

Find the $x$ and $y$-intercepts of the graph of the equation.

$y$ = $x$^{2} + 6$x$ + 5

a. | $x$-intercepts: (-1, 0), (- 5, 0); $y$-intercept: (0, - 5) | ||

b. | $x$-intercepts: (-1, 0), (- 5, 0); $y$-intercept: (0, 5) | ||

c. | $x$-intercepts: (- 5, 0); $y$-intercept: (0, 5) | ||

d. | $x$-intercept: (-1, 0); $y$-intercept: (0, 5) | ||

e. | $x$-intercepts: (1, 0), (5, 0); $y$-intercept: (0, 5) |

[Original Equation.]

Make a table of values of

^{2} + 6 | ( | |

- 6 | 5 | (- 6, 5) |

- 4 | - 3 | (- 4, - 3) |

- 2 | - 3 | (- 2, - 3) |

0 | 5 | (0, 5) |

2 | 21 | (2, 21) |

Draw the graph by plotting the points and join them with a smooth curve.

The graph crosses the

So, the

Correct answer : (2)