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Exercises Functions

Example 12 from Algebra and Trigonometry, 3.1 Functions and Function Notation

Reading Function Values from a Graph

Given the graph in Figure 4,

ⓐ Evaluate $f (2) .$
ⓑ Solve $f (x) = 4.$

Graph of a positive parabola centered at (1, 0).

Figure 4

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
ⓐ To evaluate $f (2),$ locate the point on the curve where $x = 2,$ then read the y-coordinate of that point. The point has coordinates $(2, 1),$ so $f (2) = 1.$ See Figure 5.

Figure 5

ⓑ To solve $f (x) = 4,$ we find the output value $4$ on the vertical axis. Moving horizontally along the line $y = 4,$ we locate two points of the curve with output value $4:$ $(−1, 4)$ and $(3, 4) .$ These points represent the two solutions to $f (x) = 4:$ $−1$ or $3.$ This means $f (−1) = 4$ and $f (3) = 4,$ or when the input is $−1$ or $3,$ the output is $4 .$ See Figure 6.

Figure 6

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Using Figure 4, solve $f (x) = 1.$

How did it go?

PreviousEvaluating and Solving a Tabular Function Next Determining Whether a Relationship Is a One-to-One Function

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 3.1, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.