Before you read

Answer first — see what you already know.

Function $f (x) = 5 x + 2$ .
Function $g$ is shown in the table:

$x$	$g (x)$
0	8
1	11
2	14

Which statement is true?

A
$f$ has the greater slope and the greater y-intercept
B
$g$ has the greater slope and the greater y-intercept
C
$f$ has the greater slope; $g$ has the greater y-intercept
D
$g$ has the greater slope; $f$ has the greater y-intercept

Check your answer

Answer:

Before you read

Answer first — see what you already know.

Plan A charges $$30$ per month plus $$0.10$ per text.
Plan B: $B (t) = 0.15 t + 20$ , where $t$ is number of texts.

For how many texts per month do both plans cost the same?

A
$100$
B
$200$
C
$300$
D
$500$

Check your answer

Answer:

Theory

Comparing Functions Across Representations

The SAT loves to give you two functions in different forms and ask you to compare them:

- Function $f$ : given as an equation
- Function $g$ : given as a table or graph

To compare, you need to extract the same information (slope, y-intercept, specific values) from each.

Common comparison questions:
- "Which function has the greater rate of change?"
- "Which function has the greater y-intercept?"
- "For what value of $x$ do both functions have the same value?"
- "Which function has the greater value at $x = 5$ ?"

Comparing two linear functions

Theory

Extracting Information from Each Form

Form	How to find slope	How to find y-intercept
Equation $y = mx + b$	Read $m$ directly	Read $b$ directly
Table	$\frac{\Delta y}{\Delta x}$ from any two rows	Find or calculate $f(0)$
Graph	Rise over run between two points	Read where line crosses y-axis
Verbal	Look for "per" or "each"	Look for "starts at" or "initially"

Example 1

Function $f(x) = 4x + 3$ .
Function $g$ is given by the table:

$x$	$g(x)$
0	10
2	16
4	22

Which function has the greater rate of change? Which has the greater initial value?

Function $f$ : slope $= 4$ , y-intercept $= 3$ .

Function $g$ : slope $= \frac{16 - 10}{2 - 0} = 3$ , y-intercept $= g(0) = 10$ .

Greater rate of change: $f$ ( $4 > 3$ ).

Greater initial value: $g$ ( $10 > 3$ ).

f

has the greater rate of change.

g

has the greater initial value.

Continue this lesson in the app

2 more sections including examples, practice problems, and step-by-step solutions.

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