Graph functions given a limited domain. Graph functions given a domain of all real numbers.

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# Graph functions given a limited domain. Graph functions given a domain of all real numbers. - PowerPoint PPT Presentation

Objectives. Graph functions given a limited domain. Graph functions given a domain of all real numbers. Scientists can use a function to make conclusions about the rising sea level.

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Objectives

Graph functions given a limited domain.

Graph functions given a domain of all real numbers.

Scientists can use a function to make conclusions about the rising sea level.

Sea level is rising at an approximate rate of 2.5 millimeters per year. If this rate continues, the function y = 2.5x can describe how many millimeters y sea level will rise in the next x years.

One way to understand functions such as the one above is to graph them. You can graph a function by finding ordered pairs that satisfy the function.

–x

–x

Example 1A: Graphing Solutions Given a Domain

Graph the function for the given domain.

x –3y = –6; D: {–3, 0, 3, 6}

Step 1 Solve for y since you are given values of the domain, or x.

x –3y = –6

Subtract x from both sides.

–3y = –x – 6

Since y is multiplied by –3, divide both sides by –3.

Simplify.

Example 1A Continued

Graph the function for the given domain.

Step 2 Substitute the given value of the domain for xand find values of y.

(x, y)

x

–3

(–3, 1)

0

(0, 2)

3

(3, 3)

(6, 4)

6

y

x

Example 1A Continued

Graph the function for the given domain.

Step 3 Graph the ordered pairs.

(x, f(x))

f(x) = x2–3

x

–2

(–2, 1)

f(x) = (–2)2–3 = 1

–1

(–1, –2)

f(x) = (–1)2–3 = –2

f(x) = 02 –3 = –3

(0, –3)

0

f(x) = 12–3 = –2

(1, –2)

1

f(x) = 22–3 = 1

2

(2, 1)

Example 1B: Graphing Solutions Given a Domain

Graph the function for the given domain.

f(x) = x2 – 3; D: {–2, –1, 0, 1, 2}

Step 1 Use the given values of the domain to find values of f(x).

y

x

Example 1B Continued

Graph the function for the given domain.

f(x) = x2 – 3; D: {–2, –1, 0, 1, 2}

Step 2 Graph the ordered pairs.

+2x +2x

Check It Out! Example 1a

Graph the function for the given domain.

–2x + y = 3; D: {–5, –3, 1, 4}

Step 1 Solve for y since you are given values of the domain, or x.

–2x + y = 3

y = 2x + 3

–5

y= 2(–5) + 3 = –7

(–5, –7)

(–3, –3)

–3

y= 2(–3) + 3 = –3

(1, 5)

1

y= 2(1) + 3 = 5

4

y= 2(4) + 3 = 11

(4, 11)

Check It Out! Example 1a Continued

Graph the function for the given domain.

–2x + y = 3; D: {–5, –3, 1, 4}

Step 2 Substitute the given values of the domain for xand find values of y.

(x, y)

x

y = 2x + 3

Check It Out! Example 1a Continued

Graph the function for the given domain.

–2x + y = 3; D: {–5, –3, 1, 4}

Step 3 Graph the ordered pairs.

f(x) = x2 + 2

x

(x, f(x))

(–3, 11)

–3

f(x) = (–32) + 2= 11

(–1, 3)

–1

f(x) = (–12 ) + 2= 3

f(x) = 02 + 2= 2

0

(0, 2)

1

f(x) = 12 + 2=3

(1, 3)

3

f(x) = 32 + 2=11

(3, 11)

Check It Out! Example 1b

Graph the function for the given domain.

f(x) = x2 + 2; D: {–3, –1, 0, 1, 3}

Step 1 Use the given values of the domain to find the values of f(x).

Check It Out! Example 1b

Graph the function for the given domain.

f(x) = x2 + 2; D: {–3, –1, 0, 1, 3}

Step 2 Graph the ordered pairs.

Example 2A: Graphing Functions

Graph the function –3x + 2 = y.

Step 1 Choose several values of x and generate ordered pairs.

(–2, 8)

–2

–3(–2) + 2 = 8

(–1, 5)

–3(–1) + 2 = 5

–1

(0, 2)

0

–3(0) + 2 = 2

(1, –1)

1

–3(1) + 2 = –1

(2, –4)

2

–3(2) + 2 = –4

(3, –7)

3

–3(3) + 2 = –7

Example 2A Continued

Graph the function –3x + 2 = y.

Step 2 Plot enough points to see a pattern.

Example 2A Continued

Graph the function –3x + 2 = y.

Step 3 The ordered pairs appear to form a line. Draw a line through all the points to show all the ordered pairs that satisfy the function. Draw arrowheads on both “ends” of the line.

Example 2B: Graphing Functions

Graph the function g(x) = |x| + 2.

Step 1 Choose several values of x and generate ordered pairs.

g(x) = |–2| + 2= 4

–2

(–2, 4)

g(x) = |–1| + 2= 3

(–1, 3)

–1

(0, 2)

0

g(x) = |0| + 2= 2

g(x) = |1| + 2= 3

(1, 3)

1

2

g(x) = |2| + 2= 4

(2, 4)

(3, 5)

3

g(x) = |3| + 2= 5

Example 2B Continued

Graph the function g(x) = |x| + 2.

Step 2 Plot enough points to see a pattern.

Check It Out! Example 2a

Graph the function f(x) = 3x – 2.

Step 1 Choose several values of x and generate ordered pairs.

(–2, –8)

f(x) = 3(–2) – 2 = –8

–2

(–1, –5)

–1

f(x) = 3(–1) – 2 = –5

(0, –2)

0

f(x) = 3(0) – 2 = –2

1

(1, 1)

f(x) = 3(1) – 2 = 1

2

(2, 4)

f(x) = 3(2) – 2 = 4

(3, 7)

3

f(x) = 3(3) – 2 = 7

Check It Out! Example 2a Continued

Graph the function f(x) = 3x – 2.

Step 2 Plot enough points to see a pattern.

Check It Out! Example 2b

Graph the function y = |x– 1|.

Step 1 Choose several values of x and generate ordered pairs.

y= |–2– 1| = 3

(–2, 3)

–2

–1

y= |–1 – 1| = 2

(–1, 2)

(0, 1)

0

y= |0 – 1| = 1

1

(1, 0)

y= |1 – 1| = 0

2

y= |2 – 1| = 1

(2, 1)

Check It Out! Example 2b Continued

Graph the function y = |x– 1|.

Step 2 Plot enough points to see a pattern.