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Name the three terms for the domain
x-axis / input / interval
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Name the two terms for range
y-axis / output
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Define function
Relation in which each input has one and only one output
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Determine if the domain and range of the relation and explain why.
[(-2,-1), (1,-6), (5,-1), (8,-9), (11,8)]
No repeating x values
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Determine the domain and range of the relation.
[(-3,-4), (1,6), (-9, -8), (4, -6), (-1, 9)]
Domain (x): (-3, 1, -9, 4, -1)
Range (y): (-4, 6, -8, -6, 9)
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Tell whether the relation is a function and explain why.
[(7,7), (1,7), (6,1), (11,6), (1,-8)]
Not a function, cannot have two x values
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What is a "Vertical Line Test"?
If a vertical line intersects more than once on the graph, then it is not a function.
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What sign do you use for the graph notation below?
∞, 5
[∞, 5)
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What order do you notate graph points?
(lowest, highest)
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What does it mean if you have a non-function from a vertical line test?
If it intersects, then you have two x values.
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What does the symbol below mean?
⋃
union
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When combining two domains below, what would be the long and simplified (final) answer?
∞, 0 & 0, ∞
Long answer: [∞,0) U (0,∞]
Simplified: [∞,∞]
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What does f(x) equal?
range / y-axis
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Find f(-x) when f(x) = x^2 - 2x - 2
(-x)^2 - 2(-x) - 2
x^2 + 2x -2
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Find f(-4) when f(x) = x^2 - 2x - 2
(-4)^2 - 2(-4) - 2
16 + 8 - 2 = 22
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When determining where a function might be increasing/decreasing/constant, how do you use the x- and y-values of the graph?
Refer to y-axis from left to right
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What is the slope function?
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What is the slope intercept function?
y = mx + b
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What is the point-slope function?
y - y = m(x - x)
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What is the general or standard function?
ax + by = c
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What axis is the horizontal line?
y
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What axis is the vertical line?
x-axis
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What is a common value with parallel lines?
It has the same slope
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What is the sign for slope?
m
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What does the sign below mean?
m
slope
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What slopes have negative reciprocals?
Perpendicular lines
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How do you map the slope function on a graph?
rise/run from y - axis point
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Define the slope below.
4/0
undefined
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If the line is undefined, what direction is the line going?
vertical
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What is the point-slope form of the equation of the line?
Slope = 6, passing through (-5,9)
y - 9 = 6(x - (-5))
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What is the slope-intercept form of the equation of the line of the point-slope form below?
y - 9 = 6(x-(-5))
y = 6x + 39
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If a line rises from left to right, the line has _______slope.
positive
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A line that falls from left to right has a _________ slope
negative
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The slope of a horizontal line is _____
0
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The slope of a vertical line is _________
Undefined
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The equation y=3 is a
horizontal line
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The graph of the equation x=3 is a
vertical line
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What is the vertical line test?
If a vertical line passes through an x value twice on the graph
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Find F(-4) when f(x) = x^2 - 2x - 2
(-4)^2 - 2(-4) - 2
16+8+2 = 22
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Find f(0) when f(x) = x^2 + 5 -4
0^2 + 5(0) - 4 = -4
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Find F(-x) when f(x) = x^2 - 2x - 2
(-x)^2 - 2(-x) - 2
x^2 + 2x - 2
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If you are asked f(3) = ? . What steps are there to find correct point on the graph?
refer to x-axis to find 3 first and find corresponding y-axis point below or above the x-axis
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If you are asked f(x)=4 what steps to find the correct point on the graph?
First, find 4 on the y-axis and then find corresponding x-axis point to the left or right of the y-axis
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Find the slope for the points and indicate whether the line through the points rise, fall, is horizontal or vertical. (2,4) and (3,6)
2
Line rises from left to right
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Find the slope for the points and indicate whether the line through the points rise, fall, is horizontal or vertical. (-7,5) and (-7,9)
slope is undefined
The line is vertical
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If is a line is undefined, it is what?
vertical
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If a line is vertical, it is what?
undefined
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Write the point-slope from of the line satisfying the given conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation.
Slope = 6, passing through (-5,9)
Step 1 (point-slope)
y - y1 = m(x - x1)
y - 9 = 6(x - (-5))
Step 2 (Slope-intercept form)
y - 9 = 6x + 30
y= 6x + 39
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Find the slope of the line passing through the pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal or vertical.
(-1,6) and (4,5)
Slope is negative
line falls from left to right
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Find the slope of the line passing through the pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal or vertical.
(-2,3) and (7,3)
Slope is 0
The line is horizontal
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Given the slope and y-int of the line whose equation is given. Give the steps to graph this properly.
y = -5x+1
The slope is -5
The y-intercept is 1
Step 1
Find the y-int, then from that point rise -5 and run 1
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Put the following in a linear equation in slope-intercept form and state what direction the line on the graph would be.
y=2
y = mx + 2
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Put the following in a linear equation in slope-intercept form and state the slope and what the y-intercept is.
y = 2/3x
y= 2/3x + b
slope is 2/3
y-int is 0
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Put the following in slope-intercept form and state the slope.
x = 5
y= mx + b
y = m5 + 0
- y2 - y1 = 1 + 0 (When y is zero, use 1+0)
- _________________________________
- x2 - x1 = 5- 5
1/0 = undefined
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Write an equation of the line
Horizontal: through (0, -3)
What is the equation of the line in standard form?
ax + by = c
x=c
x + (-3) = 0
x = 0/3 = 0
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a. Rewrite the equation 2x + y + 1 = 0 in slope-int form.
b. Give the slope and y-int
c. List steps to graph the slope and y-int
- a. 2x+y+1 = 0
- y = -2x - 1
- c. y = -1
- m = -2 = -2 / 1 = RISE/RUN
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Determine the x and y intercepts with the equation below.
solve x
- 5x + 5y + 25 = 0
- 5x + 5(0) + 25 = 0
- 5x + 25 = 0
- 5x = -25
- x = -5
- Solve for y
- 5x + 5y + 25 = 0
- 5(0) + 5y + 25 = 0
- 5y + 25 = 0
- 5y = -25
- y=-5
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Find the slope of the line that is (a) parallel and (b) perpendicular to the line through the pair of points.
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