Back to Interpret the equation y = mx + b as defining a linear function — Problem 5 · Task Set 16

Exercises: Linear and Nonlinear Functions

Work through each section in order. Show your work where indicated. For each function, remember the key test: a function is linear when its rate of change is constant.

Grade 8·22 problems·~30 min·Common Core Math - Grade 8·container·8-f-a-3

Work through problems with immediate feedback

Fluency Practice

For $y = x^2$ , complete the table of changes in $y$ . From $x=1$ to $x=2$ : $y$ goes $1 \to 4$ , change ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ . From $x=2$ to $x=3$ : $y$ goes $4 \to 9$ , change ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ . From $x=3$ to $x=4$ : $y$ goes $9 \to 16$ , change ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .

first change:

second change:

third change: