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Warm-up

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

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Warm-up

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

  2. 10.8 Compare Linear, Exponential, and Quadratic Models Students will Compare Linear, Exponential, and Quadratic Models

  3. 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

  4. Examples: • LINEAR, QUADRATIC or EXPONENTIAL? • y = 6x + 3 • y = 7x2 +5x – 2 • 9x + 3 = y • 42x = 8

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

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

  7. Is the table linear, quadratic or exponential? • 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

  8. x – 2 – 1 0 2 1 y – 2 4 10 1 7 ANSWER The table of values represents a linear function. EXAMPLE 2 Identify functions using differences or ratios b. Differences:3 3 3 3

  9. ANSWER The table of values represents a quadratic 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. First differences:0 2 4 6 Second differences:2 2 2

  10. 0 y 2 x – 2 – 1 1 0.08 0.4 10 ANSWER exponential function for Examples 1 and 2 GUIDED PRACTICE 2. Tell whether the table of values represents a linear function, an exponential function, or a quadratic function.

  11. Is the table linear, quadratic or exponential?

  12. x –2 –1 0 2 1 y 2 0 2 0.5 0.5 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.

  13. x –2 –1 0 2 1 y 2 0 2 0.5 0.5 EXAMPLE 3 Write an equation for a function SOLUTION Determine which type of function the table of values represents. STEP1 First differences:–1.5 –0.5 0.5 1.5 Second differences:1 1 1

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