Functions
GradesGrade 8FunctionsEvaluating & Comparing Functions

Evaluating & Comparing Functions

🔗 Functions
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Evaluating & Comparing Functions

Evaluate functions using notation f(x), and compare functions given in different representations.

To evaluate a function, substitute the given input value for the variable and simplify. Functions can be represented as equations, tables, graphs, or verbal descriptions — you should be able to compare any two representations.

f(x)=3x−2⇒f(4)=3(4)−2=10f(x) = 3x - 2 \Rightarrow f(4) = 3(4) - 2 = 10
🔁Comparing functions in different forms
Function A (equation): f(x) = 2x + 1 → slope = 2

Function B (table):
x: 0  1  2  3
y: 3  5  7  9 → slope = (5−3)/(1−0) = 2, y-intercept = 3

Function B has the greater y-intercept (3 > 1).
mB=5−31−0=2bB=3>bA=1m_B = \frac{5-3}{1-0} = 2 \quad b_B = 3 > b_A = 1

Comparing two functions from different representations:

1Identify the slope (rate of change) from each representation
2Identify the y-intercept (initial value) from each
3Compare slopes — steeper slope means faster rate of change
4Compare y-intercepts — larger y-intercept means higher starting value
5State your conclusion with reference to the context
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Remember This!

When finding slope from a table, always use two points and compute (Δy) / (Δx). The difference should be constant for a linear function.

✏ī¸ Try It!

Given f(x) = −3x + 7, what is f(−2)?

Practice with CalcVerse
📈Line Grapher (y = mx + b)
Take Quiz 📝 — 25 Questions