Warm-up 1. Graph y = 3x. ANSWER Tell whether the ordered pairs (0, 0), (1, 2), (2, 4), and (3, 6) represent a linear function. 2. For y = x2 – 3x – 5, find corresponding y-values for the x-values –2, 1, and 3. 3.

10.8 Compare Linear, Exponential, and Quadratic Models Students will Compare Linear, Exponential, and Quadratic Models

Identifying from an equation: Linear Has an x with no exponent. y = 5x + 1 y = ½x 2x + 3y = 6 Quadratic Has an x2 in the equation. y = 2x2 + 3x – 5 y = x2 + 9 x2 + 4y = 7 Exponential Has an x as the exponent. y = 3x + 1 y = 52x 4x + y = 13

Examples: LINEAR, QUADRATIC or EXPONENTIAL? y = 6x + 3 y = 7x2 +5x – 2

Identifying from a graph: Linear Makes a straight line Quadratic Makes a U or ∩ Exponential Rises or falls quickly in one direction

LINEAR, QUADRATIC or EXPONENTIAL? a) b) c) d)

Is the table linear, quadratic or exponential? y changes more quickly than x. Never see the same y value twice. Common multiplication pattern Linear Never see the same y value twice. 1st difference is the same Quadratic See same y more than once. 2nd difference is the same

EXAMPLE 2 Identify functions using differences or ratios b. x – 2 – 1 1 2 y 4 7 10 Differences: 3 3 3 3 ANSWER The table of values represents a linear function.

EXAMPLE 2 Identify functions using differences or ratios Use differences or ratios to tell whether the table of values represents a linear function, an exponential function, or a quadratic function. a. x –2 –1 1 2 y –6 –4 6 First differences: 0 2 4 6 Second differences: 2 2 2 ANSWER The table of values represents a quadratic function.

GUIDED PRACTICE for Examples 1 and 2 2. Tell whether the table of values represents a linear function, an exponential function, or a quadratic function. y 2 x – 2 – 1 1 0.08 0.4 10 ANSWER exponential function

x y -5 1 -4 2 -1 3 4 11 x y -2 -1 -4 -8 2 -32 5 -256

Is the table linear, quadratic or exponential? y 1 2 -1 3 4 5 8 x y 1 3 2 9 27 4 81 5 243 x y 1 5 2 9 3 13 4 17 21

EXAMPLE 3 Write an equation for a function Tell whether the table of values represents a linear function, an exponential function, or a quadratic function. Then write an equation for the function. x –2 –1 1 2 y 0.5

EXAMPLE 3 Write an equation for a function SOLUTION STEP 1 Determine which type of function the table of values represents. x –2 –1 1 2 y 0.5 First differences: –1.5 –0.5 0.5 1.5 Second differences: 1 1 1