Question

Use the graph to determine which statement describes f(x)

O A. f(x) does not have an inverse function, because its graph fails the
horizontal line test.
O B. f(x) has an inverse function, because its graph passes the
horizontal line test.
C. f(x) has an inverse function, because its graph passes the vertical
line test.
D. f(x) does not have an inverse function, because its graph fails the
vertical line test.

Answer 1

f(x) does not have an inverse function, because its graph fails the horizontal line test. ⇒ A

Explanation:

The vertical line test is used to show that the graph represents a

function or not

• If the vertical line crosses the graph in more than one point, then the graph does not represent a function

• If the vertical line crosses the graph in only one point in different positions, then the graph represents a function

The horizontal line test is used to show that the function has an

inverse or not

• If the horizontal line crosses the graph of a function in more than one point, then the function has no inverse

• If the horizontal line crosses the graph of a function in only one point in different positions, then the function has an inverse

Let us look at the given graph

→ The graph represents a parabola, which represents the function f(x)

∵ Any horizontal line drawn will cross the graph in more than one point

∴ f(x) has no inverse

∴ f(x) does not have an inverse function, because its graph fails the

horizontal line test.