Evaluating Functions With Graphs

High school student reviewing algebra equations on a digital tablet

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What does  ƒ(x) mean? Think of the function notation as a replacement for y. It reads "f of x."

  • ƒ(x) = 2x + 1 is also known as y = 2x + 1.
  • ƒ(x) = |-x + 5| is also known as y = |-x + 5|.
  • ƒ(x) = 5x2 + 3x - 10 is also known as y = 5x2 + 3x - 10.

Other Versions of Function Notation

What do these variations of notation share? 

  • ƒ(t) = -2t2
  • ƒ(b) = 3eb
  • ƒ(p) = 10p + 12

Whether the function begins with ƒ(x) or ƒ(t) or ƒ(b) or ƒ(p) or ƒ(♣), it means that the outcome of ƒ depends on what's in the parentheses.

  • ƒ(x) = 2x + 1 (The value of ƒ(x) depends on the value of x.)
  • ƒ(b) = 3eb (The value of ƒ(b) depends on the value of b.)

Learn how to use a graph to find specific values of ƒ. 

01
of 06

Linear Function

What is ƒ(2)?

In other words, when x = 2, what is ƒ(x)?

Trace the line with your finger until you get to the part of the line where x = 2. What is the value of ƒ(x)?

Answer: 11

 

02
of 06

Absolute Value Function

What is ƒ(-3)?

In other words, when x = -3, what is ƒ(x)?

Trace the graph of the absolute value function with your finger until you're touching the point where x = -3. What is the value of ƒ(x)?

Answer: 15

 

03
of 06

Quadratic Function

What is ƒ(-6)?

In other words, when x = -6, what is ƒ(x)?

Trace the parabola with your finger until you touch the point at which x = -6. What is the value of ƒ(x)?

Answer: -18

 

04
of 06

Exponential Growth Function

What is ƒ(1)?

In other words, when x = 1, what is ƒ(x)?

Trace the exponential growth function with your finger until you touch the point at which x = 1. What is the value of ƒ(x)?

Answer: 3

 

05
of 06

Sine Function

What is ƒ(90°)?

In other words, when x = 90°, what is ƒ(x)?

Trace the sine function with your finger until you touch the point at which x = 90°. What is the value of ƒ(x)?

Answer: 1

 

06
of 06

Cosine Function

What is ƒ(180°)?

In other words, when x = 180°, what is ƒ(x)?

Trace the cosine function with your finger until you touch the point at which x = 180°. What is the value of ƒ(x)?

Answer: -1