Determining if a Relation is a Function

a

Let's substitute $0$ for $x$ and evaluate.

y = 3 x - 2

x = 0

y = 3 \cdot 0 - 2

y = - 2

The value of $y$ is $- 2$ for $x = 0 .$

b

Similarly, we substitute $- 2$ for $x$ and evaluate.

y = 3 x - 2

x = - 2

y = 3 (- 2) - 2

a (- b) = - a \cdot b

y = - 6 - 2

SubTermSubtract term

y = - 8

Thus, $y = - 8$ when $x = - 2 .$

c

To solve $y = 7,$ we substitute $7$ for $y .$ This gives an equation with one unknown, $x .$

y = 3 x - 2

y = 7

7 = 3 x - 2

LHS + 2 = RHS + 2

9 = 3 x

RearrangeEqnRearrange equation

3 x = 9

LHS / 3 = RHS / 3

x = 3

The solution to the equation is $x = 3 .$

Determining if a Relation is a Function 1.8 - Solution