1­2 Analyzing Graphs of Functions and Relations - PC\|MAC

[Pages:12]Pre Cal 12 Lesson with notes 5th.notebook

12 Analyzing Graphs of Functions and Relations

August 18, 2016

Learning Targets: I can use graphs of functions to estimate function values and find domains, ranges, yintercepts, and zeros of functions I can explore symmetries of graphs, and identify even and odd functions

The linear graph of a function for net profit/loss given x units sold has an xintercept of 200. What does this mean?

A graph of marathon times given resting time prior to the race decreases and then increases with a minimum at two days. If marathon times are the dependent variable and resting time is the independent variable, what does this mean?

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Pre Cal 12 Lesson with notes 5th.notebook

August 18, 2016

Graph of a function: set of ordered pairs (x, f(x)) such that x is in the domain of f.

x = directed distance from yaxis f(x) = directed distance from the xaxis

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Pre Cal 12 Lesson with notes 5th.notebook

You can use a graph to estimate function values.

August 18, 2016

Example 1

1. The function f(x) = 5x2 + 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.

a. Use the graph to estimate the profit when marketing costs are $30,000. Confirm your estimate algebraically.

b. Use the graph to estimate marketing costs when the profit is $1,250,000. Confirm your estimate algebraically.

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2. An investor assessed the average daily value of a share of a certain stock over a 20day period. The value of the stock can be approximated by v(d) = 0.002d4 0.11d3 + 1.77d2 8.6d + 31,

of the assessment. 0 d 20, where d represents the day a. Use the graph to estimate the value of the stock on the 10th day. Confirm your estimate algebraically.

b. Use the graph to estimate the days during which the stock was valued at $30 per share. Confirm your estimate algebraically.

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Pre Cal 12 Lesson with notes 5th.notebook

August 18, 2016

The domain and range of a function can also be determined from the graph. Unless the graph of a function is bounded on the left by a circle or a dot, you can assume that the function extends beyond the edges of the graph.

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Pre Cal 12 Lesson with notes 5th.notebook

Example 2: Find the domain and range of the function.

August 18, 2016

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Find the domain and range of the function

7. h(x) = 8. g(x) = |x 1|

Dots (open or closed) at the extreme left and right points of a graph indicate that the graph does not extend beyond these points. When no dots are shown, assume the graph extends beyond these points.

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Pre Cal 12 Lesson with notes 5th.notebook

August 18, 2016

The yintercept of a function is where the graph crosses the yaxis, to find it look on the graph, if given. To solve algebraically, set x = 0 and solve for y.

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Pre Cal 12 Lesson with notes 5th.notebook

August 18, 2016

Example 3: Use the graph of each function to approximate the y intercept. Then find the yintercept algebraically.

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Use the graph of each function to approximate its yintercept. Then find the yintercept algebraically.

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Pre Cal 12 Lesson with notes 5th.notebook

August 18, 2016

The xintercept(s) of a function are called the zero(s) of a function and are the roots of the function. To find them when the function is graphed, look at where it crosses the xaxis. To find them algebraically, set y equal to zero and solve.

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Example 4: Use the graph to approximate its zeros. Then find its zeros algebraically.

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