Graphs of Functions and Equations Worksheet

Graphs of Functions and Equations Worksheet
  • Page 1
 1.  
Find the x and y-intercepts of the graph of the equation.
y = x3 - 8
a.
x-intercept: (0, 0); y-intercept: (2, - 8)
b.
x-intercept: (0, 2); y-intercept: (- 8, 0)
c.
x-intercept: (22, 0); y-intercept: (0, 8)
d.
x-intercept: (2, 0); y-intercept: (0, - 8)
e.
x-intercept: (38, 0); y-intercept: (0, 8)


Solution:

y = x3 - 8
[Original Equation.]

Make a table of values of (x, y)
xy = x3 - 8(x, y)
- 1- 9(- 1, - 9)
0- 8(0, - 8)
1- 7(1, - 7)
20(2, 0)
319(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).


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


Solution:

The tangent function is f(x) = tan x

Graph 4 represents the tangent function.


Correct answer : (5)
 3.  
Sketch the graph of the equation y = 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
xy = x+9(x, y)
- 90(- 9, 0)
- 61.7(- 6, 1.7)
- 32.4(- 3, 2.4)
03(0, 3)
33.5(3, 3.5)
63.9(6, 3.9)



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

The y intercept is (0, 3).


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


Solution:

The secant function is f(x) = sec x

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)


Solution:

The graph crosses the x-axis at the origin.

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


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


Solution:

The cube root function is f(x) = x3

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


Solution:

The exponential function is f(x) = ex

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


Solution:

The logarithmic function is f(x) = log x

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


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.


Correct answer : (5)
 10.  
Find the x and y-intercepts of the graph of the equation.
y = x2 + 6x + 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.
xy = x2 + 6x + 5(x, y)
- 65(- 6, 5)
- 4- 3(- 4, - 3)
- 2- 3(- 2, - 3)
05(0, 5)
221(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).


Correct answer : (2)

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