How do you find a function value for x? How do you do that on a calculator? If f (x) = x ²– 2x – 8, find the function value for f (3). Answer:–5

Was that too easy? If f (x) = x ² – 2x – 8, find the function value for f (–3d). Answer:9d ² + 6d – 8

Okay, still too easy? If f (x) = x ² – 2x – 8, find the function value for f (2a – 1). Answer:4a ² – 8a – 5

If, find f (6). A. B. C. D.

What is the domain of a function? Problems: No zeros in the denominator. No negatives under the radical (not real). State the domain of the function. Answer:all real numbers x such that x ≥, or

State the domain of the function. Answer: The denominator can not be zero

State the domain of the function. Answer: or

Piecewise Functions Realtors in a metropolitan area studied the average home price per square foot as a function of total square footage. Their evaluation yielded the following piecewise-defined function. Find the average price per square foot for a home with the square footage of 1400 square feet. Answer: $85 per square foot

A, B, C or D? The cost of residential electricity use can be represented by the following piecewise function, where k is the number of kilowatts. Find the cost of electricity for 950 kilowatts. A.$47.50 B.$48.00 C.$57.50 D.$76.50

1.2 Roots Symmetry Zeroes Odd/Even Functions

Use graphs of functions to estimate function values and find domains, ranges, y-intercepts, and zeros of functions. Explore symmetries of graphs, and identify even and odd functions. Review of Functions

The function f (x) = –5x ² + 50x approximates the profit at a toy company, where x is marketing costs and f (x) is profit. Both costs and profits are measured in tens of thousands of dollars. Use the graph to estimate the profit when marketing costs are $30,000. Confirm your estimate algebraically. Answer: $1,050,000

Example 1 Answer: $1,050,000 $30,000 is three ten thousands. The function value at x = 3 appears to be about 100 ten thousands, so the total profit was about $1,000,000. To confirm this estimate algebraically, find f(3). f(3) =  5(3) (3) = 105, or about $1,050,000. The graphical estimate of about $1,000,000 is reasonable.

Graphs restricted by an interval. A-Z Toy Boat Company found the average price of its boats over a six month period. The average price for each boat can be represented by the polynomial p (x) = –0.325x³ + 1.5x² + 22, where x is the month, and 0 < x ≤ 6. Use the graph to estimate the average price of a boat in the fourth month. Confirm you estimate algebraically. A.$25 B.$23 C.$22 D.$20

Use the graph of f to find the domain and range of the function. Answer: D: R:

Use the graph of f to find the domain and range of the function. *[1] instead of [2] in the answers A.Domain: Range: B.Domain: Range: C.Domain: Range: D.Domain: Range:

Use the graph of the function g (x) =│x + 2│– 3 to approximate its y-intercept. Then find the y-intercept algebraically.

Use the graph of the function to approximate its y-intercept. A.–1; f (0) = –1 B.0; f (0) = 0 C.1; f (0) = 1 D.2; f (0) = 2

Use the graph of f (x) = x ³ – x to approximate its zero(s). Then find its zero(s) algebraically.

A.–2.5 B.–1 C.5 D.9 Use the graph of to approximate its zero(s). Then find its zero(s) algebraically.

Tests for symmetry

Examples of odd and even functions

Use the graph of the equation y = x ² + 2 to test for symmetry with respect to the x-axis, the y-axis, and the origin. Answer:symmetric with respect to the y-axis

Use the graph of the equation xy = –6 to test for symmetry with respect to the x-axis, the y-axis, and the origin. Support the answer numerically. Then confirm algebraically. Answer:symmetric with respect to the origin

Example 5 Use the graph of the equation y = –x ³ to test for symmetry with respect to the x-axis, the y- axis, and the origin. Support the answer numerically. Then confirm algebraically. A.symmetric with respect to the x-axis B.symmetric with respect to the y-axis C.symmetric with respect to the origin D.not symmetric with respect to the x-axis, y-axis, or the origin

Odd and Even Functions

Graph the function f (x) = x ² – 4x + 4 using a graphing calculator. Analyze the graph to determine whether the function is even, odd, or neither. Confirm algebraically. If even or odd, describe the symmetry of the graph of the function. Answer: neither

Graph the function f (x) = x ² – 4 using a graphing calculator. Analyze the graph to determine whether the function is even, odd, or neither. Confirm algebraically. If even or odd, describe the symmetry of the graph of the function. Answer: even; symmetric with respect to the y-axis

Graph the function f (x) = x ³ – 3x ² – x + 3 using a graphing calculator. Analyze the graph to determine whether the function is even, odd, or neither. Confirm algebraically. If even or odd, describe the symmetry of the graph of the function. Answer: neither

Assignment Due Monday Pg. 9: 1,8,11,13,16,30,39-45 odds,48 Pg. 19: 1,4,9,12,16,26,29,34,37

Answers 5.

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