Relations and Functions
In your own words, what are domain and range?
domain= x-values
range = y-values
Is the following function a linear function? Explain why or why not. g(x)= 2x - 5
Yes. There are not exponents, multiplication of two variables, division by a variable, or square roots!
What is the slope formula?
Y2-Y1/X2-X1
What is slope intercept form?
y = mx+b
What is the range of the following relation? Is this a function? {(-3, 2), (4, 1), (0,3), (5, -2), (2, 7)}
range= {-2, 1, 2, 3, 7}, yes it is a function.
State the domain of the relation and range of the following relation. {(-3, -4), (-1, 0), (3, 0), (5, 3)}
domain= {-3, -1, 3, 5}
range= {-4, 0, 3}
What is standard form and what are the two requirements to be in standard form?
Ax + By = C
A must be positive and A, B, and C must be integers (no fractions)
How can you find slope on a graph?
Rise over run
Write an equation in slope intercept form for the line described. slope = 4/3 passes through (0, 4)
What is y=(4/3)x + 4
Is 2x2 -9 a linear function? Why or why not?
No. There is an exponent greater than 1.
Is the following relation a function. Explain your answer. {(2, 21), (2, 25), (8, 30)}
No. The x-value of 2 repeats.
Put the following equation into standard form.
Identify A, B, and C.
y=3x - 9
y = 3x - 9
3x - y = 9
A = 3,
B = -1,
C = 9
Find the slope of the following points. (-1, 4) and (1, -2)
m=-3
Use slope-intercept form to write an equation of the line that passes through (-2, -1) with a slope of -3.
y - y2 = -3(x - x2)
y - - 1 = -3(x - -2)... y + 1 = -3x - 6
y= -3x - 7
What is point slope form?
y - y1 = m(x - x1)
What is the vertical line test? How do you use it?
The vertical line test determines if a graph is a function or not. You put your pencil on the graph and move it from left to right. If it touches the graph in more than one spot at a time, then the graph is not a function.
Find the x-intercept and y-intercept of the graph 2x+5y=10.
x-intercept: 2x + 5*(0) = 10 , 2x = 10 x = 5
(5,0)
y-intercept: 2(0) + 5y = 10, 5y = 10, y = 2
(0,2)
Find the equation of a line that is parallel to y = 5x - 7 and passes through the point (-8, 11)
m = 5 y - y1 = 5(x - x1)
y - 11 = 5(x - - 8)
y = 5x + 40 + 11
y=5x+51
Write an equation of the the line that passes through the points (2, -3) and (-3, 7).
m = 7 - - 3/-3 - 2, m = 10/-5, m = -2
Choose either point y -7 = -2(x + 3)
y - 7 = -2x - 6
y= -2x + 1
Write an equation in slope-intercept form for a line that passes through (12, 0) and is parallel to y=(-1/2)x - 3.
y= (-1/2)x + 6
Evaluate the following function for f(3). f(x)= -4x^2 -2x +5
-37
Find the x-intercept and the y-intercept of the graph of -2x + y - 4 = 0.
x-intercept:
2x - y = -4, 2x - 0 - -4, 2x = -4,
(-2, 0)
y-intercept(, 2(0) + y = -4, y = -4
(0,4)
If a graph passes through the points (-2, 0) and (0, -3), what is the slope of that line?
m = y2 - y1/x2 - x1
m =-3 - 0/0 - - 2
m=-3/2
Write an equation in slope-intercept form for the line that passes through (3, -2) and is perpendicular to the line with equation y= -5x +1.
You should be getting fractions!
m = 1/5
y - -2 = 1/5(x - 3).. y + 2 = 1/5x - 3/5
y = 1/5x - 3/5 - 10/5
y = (1/5)x - (13/5)
Graph the line on your whiteboard.
6y=3x+9
m= 1/2
b=3