Answered: "Which of the following graphs represent functions that..."

angepepagiortzb

Answered question

2021-11-23

Which of the following graphs represent functions that have inverse functions?

Answer & Explanation

Robert Harris

Beginner2021-11-24Added 23 answers

Step 1: Horizontal line test:
Horizontal line test is used to determine whether a function has inverse or not.
We draw the graph of given function and check is there any horizontal line that can intersect the graph in more than 1 point.
If no horizontal line intersects graph in more than 1 point, we say, the function has an inverse.
If any horizontal line intersect the graph in more than 1 point, the function does not have an inverse.
Let us check given graphs one by one
Step 2: (a)
For the given graph,

if we draw horizontal line, it intersects the graph in two distinct points
So horizontal line test fails.
Hence, function represented by given graph does not have an inverse function.
Step 3: (b)
For the given graph,

if we draw any horizontal line, it intersects the graph in only one point.
So the graph passes the horizontal line test.
Hence, function represented by given graph has an inverse function.
Step 4: (c)
For the given graph,

if we draw any horizontal line, it intersects the graph in only one point.
So the graph passes the horizontal line test.
Hence, function represented by given graph has an inverse function.

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