Transcript Lesson 2-2
Five-Minute Check (over Lesson 2–1)
Then/Now
New Vocabulary
Example 1: Identify Linear Functions
Example 2: Real-World Example: Evaluate a Linear Function
Key Concept: Standard Form of a Linear Equation
Example 3: Standard Form
Example 4: Use Intercepts to Graph a Line
Over Lesson 2–1
Determine whether the relation is a
function. If it is a function, determine
if it is one-to-one, onto, both, or
neither.
A. function; one-to-one
D. not a function
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B
A
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A
B
C
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D
D
C. function; both
C
B. function; onto
A.
B.
C.
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D.
Over Lesson 2–1
Determine whether the relation is
a function. If it is a function,
determine if it is one-to-one,
onto, both, or neither.
C. function; both
D. not a function
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B
A
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A
B
C
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D
D
B. function; onto
A.
B.
C.
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D.
C
A. function; one-to-one
Over Lesson 2–1
Determine whether the relation is a function. If it is
a function, determine if it is one-to-one, onto, both,
or neither.
{(1, 2), (2, 1), (5, 2), (2, 5)}.
A. function; one-to-one
D. not a function
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B
A
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A
B
C
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D
D
C. function; both
C
B. function; onto
A.
B.
C.
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D.
Over Lesson 2–1
Find f(–3) if f(x) = x2 + 3x + 2.
A. 20
B. 10
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A
B
C
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D
D
A
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B
D. –2
C
C. 2
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B.
C.
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D.
Over Lesson 2–1
What is the value of f(3a) if f(x) = x2 – 2x + 3?
A. 3a + 3
B. 3a2 – 6a + 3
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A
B
C
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D
D
A
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B
D. 9a2 – 6a + 3
C
C. 9a2 – 2a + 3
A.
B.
C.
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D.
You analyzed relations and functions.
(Lesson 2–1)
• Identify linear relations and functions.
• Write linear equations in standard form.
• linear relations
• linear equation
• linear function
• standard form
• y-intercept
• x-intercept
Identify Linear Functions
A. State whether g(x) = 2x – 5 is a linear function.
Write yes or no. Explain.
Answer: Yes; this is a linear function because it is in the
form g(x) = mx + b; m = 2, b = –5.
Identify Linear Functions
B. State whether p(x) = x3 + 2 is a linear function.
Write yes or no. Explain.
Answer: No; this is not a linear function because x has
an exponent other than 1.
Identify Linear Functions
C. State whether t(x) = 4 + 7x is a linear function.
Write yes or no. Explain.
Answer: Yes; this is a linear function because it can be
written as t(x) = mx + b; m = 7, b = 4.
A. State whether h(x) = 3x – 2 is a linear function.
Explain.
A. yes; m = –2, b = 3
B. yes; m = 3, b = –2
A
B
C
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D
D
A
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B
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D. No; there is no slope.
C
C. No; x has an exponent
other than one.
A.
B.
C.
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D.
B. State whether f(x) = x2 – 4 is a linear function.
Explain.
A. yes; m = 1, b = –4
B. yes; m = –4, b = 1
A
B
C
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D
D
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B
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A
D. No; x has an exponent
other than one.
C
C. No; two variables are
multiplied together.
A.
B.
C.
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D.
C. State whether g(x, y) = 3xy is a linear function.
Explain.
A. yes; m = 3, b = 1
B. yes; m = 3, b = 0
A
B
C
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D
D
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B
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A
D. No; x has an exponent
other than one.
C
C. No; two variables are
multiplied together.
A.
B.
C.
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D.
Evaluate a Linear Function
A. METEOROLOGY The linear function
f(C) = 1.8C + 32 can be used to find the number of
degrees Fahrenheit f(C) that are equivalent to a
given number of degrees Celsius C.
On the Celsius scale, normal body temperature is
37C. What is it in degrees Fahrenheit?
f(C) = 1.8C + 32
Original function
f(37) = 1.8(37) + 32
Substitute.
= 98.6
Simplify.
Answer: Normal body temperature, in degrees
Fahrenheit, is 98.6°F.
Evaluate a Linear Function
B. METEOROLOGY The linear function
f(C) = 1.8C + 32 can be used to find the number of
degrees Fahrenheit f(C) that are equivalent to a
given number of degrees Celsius C.
There are 100 Celsius degrees between the freezing
and boiling points of water and 180 Fahrenheit
degrees between these two points. How many
Fahrenheit degrees equal 1 Celsius degree?
Divide 180 Fahrenheit degrees by 100 Celsius degrees.
Answer: 1.8°F = 1°C
C. 2 miles
A
D. 0.5 miles
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D
B. 5 miles
B
A. 50 miles
A
B
C
D
C
A.
B.
C.
D.
A
D. 15 seconds
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D
C. 5 seconds
A
B
C
D
C
B. 1.67 seconds
B
A. 0.6 second
A.
B.
C.
D.
Standard Form
Write y = 3x – 9 in standard form. Identify A, B,
and C.
y = 3x – 9
Original equation
–3x + y = –9
Subtract 3x from each side.
3x – y = 9
Multiply each side by –1 so
that A ≥ 0.
Answer: 3x – y = 9; A = 3, B = –1, and C = 9
Write y = –2x + 5 in standard form.
A. y = –2x + 5
B. –5 = –2x + y
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B
A
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A
B
C
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D
D
D. –2x – 5 = –y
C
C. 2x + y = 5
A.
B.
C.
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D.
Use Intercepts to Graph a Line
Find the x-intercept and the y-intercept of the graph
of –2x + y – 4 = 0. Then graph the equation.
The x-intercept is the value of x when y = 0.
–2x + y – 4 = 0
Original equation
–2x + 0 – 4 = 0
Substitute 0 for y.
–2x = 4
x = –2
Add 4 to each side.
Divide each side by –2.
The x-intercept is –2. The graph crosses the x-axis at
(–2, 0).
Use Intercepts to Graph a Line
Likewise, the y-intercept is the value of y when x = 0.
–2x + y – 4 = 0
Original equation
–2(0) + y – 4 = 0
Substitute 0 for x.
y =4
Add 4 to each side.
The y-intercept is 4. The graph crosses the y-axis
at (0, 4).
Use Intercepts to Graph a Line
Use the ordered pairs to graph this equation.
Answer: The x-intercept is –2, and the y-intercept is 4.
What are the x-intercept and the y-intercept of the
graph of 3x – y + 6 = 0?
A. x-intercept = –2
y-intercept = 6
A
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B
D. x-intercept = –6
y-intercept = 2
A
B
C
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D
D
C. x-intercept = 2
y-intercept = –6
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B.
C.
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D.
C
B. x-intercept = 6
y-intercept = –2