Graphs of Functions and Equations Worksheet

Graphs of Functions and Equations Worksheet
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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)

Solution:

y = x3 - 8
[Original Equation.]

Make a table of values of (x, y)
 x y = x3 - 8 (x, y) - 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 x-axis at x = 2 and y-axis at y = - 8.

So, the x-intercept is (2, 0) and y-intercept is (0, - 8).

2.
Identify the basic tangent function from the graphs.

 a. Graph 5 b. Graph 1 c. Graph 2 d. Graph 3 e. Graph 4

Solution:

The tangent function is f(x) = tan x

Graph 4 represents the tangent function.

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)

Solution:

y = x+9
[Original Equation.]

Make a table of values of x and y
 x y = x+9 (x, y) - 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 y intercept is (0, 3).

4.
Identify the basic secant function from the graphs.

 a. Graph 3 b. Graph 4 c. Graph 1 d. Graph 2 e. Graph 5

Solution:

The secant function is f(x) = sec x

Graph 5 represents the secant function.

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)

Solution:

The graph crosses the x-axis at the origin.

So, the x-intercept of the graph is (0, 0).

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

Solution:

The cube root function is f(x) = x3

Graph 3 represents the cube root function.

7.
Identify the basic exponential function from the graphs.

 a. Graph 2 b. Graph 5 c. Graph 3 d. Graph 1 e. Graph 4

Solution:

The exponential function is f(x) = ex

Graph 1 represents the exponential function.

8.
Identify the basic logarithmic function from the graphs.

 a. Graph 5 b. Graph 3 c. Graph 1 d. Graph 2 e. Graph 4

Solution:

The logarithmic function is f(x) = log x

Graph 2 represents the logarithmic function.

9.
Identify the constant function from the graphs.

 a. Graph 5 b. Graph 4 c. Graph 1 d. Graph 2 e. Graph 3

Solution:

In Graph 3, for every value of x, the corresponding y value always the same. That is 10.

Graph 3 represents the constant function.

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)

Solution:

y = x2 + 6x + 5
[Original Equation.]

Make a table of values of x and y.
 x y = x2 + 6x + 5 (x, y) - 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 x-axis at x = -1, x = - 5 and y-axis at y = 5.

So, the x-intercepts are (-1, 0), (- 5, 0) and y-intercept is (0, 5).