Question

1. Using the graph of the function f(x) shown below, answer the following questions.
(a) Find the value of each of the following:
f(-7)= f(0)=
f(4)= f(9)=
(b) For how many values of x does f(x)=5?Illustrate on the graph.
(c) What is the y-intercept of this relation?
(d) State the maximum and minimum values the graph obtains.
(e) Explain why the graph above represents a function.

Answer 1

Graphs can be used to represent functions, and vice verse

• The values of f(-7), f(0), f(4) and f(9) are -6, 3, 1 and -4, respectively.
• f(x) = 5 illustrate three values of x
• The y-intercept is 3
• The maximum and the minimum values of the graph are 5.5 and 6
• The graph passes the vertical line test.

(a) The values of f(-7), f(0), f(4) and f(9)

• At x = -7, the corresponding value of the function is -6.
• At x = 0, the corresponding value of the function is 3.
• At x = 4, the corresponding value of the function is 1
• At x = 9, the corresponding value of the function is -4

Hence, the values of f(-7), f(0), f(4) and f(9) are -6, 3, 1 and -4, respectively.

(b) The number of values of the x at f(x) = 5

At f(x) =5, the values of x are -10, 1 and 3.

Hence, f(x) = 5 illustrate three values of x

(c) The y-intercept

This is the point where the graph crosses the y-axis, i.e. when x = 0.

Hence, the y-intercept is 3

(d) The maximum and the minimum values of the graph

The highest point on the graph is (2.5,5.5), while the least point is (-7,-6)

Hence, the maximum and the minimum values of the graph are 5.5 and 6, respectively.

(e) Why the graph represents a function

It represents a function because it passes the vertical line test.

This in other words means that, each x value has exactly one y value

Read more about functions and graphs at:

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