FUNCTIONS
Linear Functions
Function Notation
Graphing Linear Equations
Standard Form
100
Is this graph a function? Explain.
Yes, it is. The vertical line test will only go through one point at a time. The x-values do not repeat.
100
Is the function linear or non-linear? Explain.
Non-linear. Graph is not a straight line.
100
Evaluate the following:
f(x) = -3x + 5 when x = -2
11
100
What are the x and y intercepts:
3x - 2y = -6
x-intercept?
y-intercept?
x-intercept = (-2, 0)
y-intercept = (0, 3)
100
Describe the transformation done to the function:
(vertical, horizontal or flip? and Left?, Right?, Up?, or Down, or x axis or y axis?)
f(x) = x + 3 starting function
g(x) = f(x) + 4 transformation of starting function
Vertical, and up 4
200
The function y = -3x + 12 represents the amount y (in fluid ounces) water left in a bottle after taking x gulps.
Which is the dependent variable?
Which is the independent variable?
Dependent variable: amount of water left in a bottle
Independent variable: number of gulps taken
200
Does the table represent a linear or non-linear function? Explain.
Linear. The inputs and outputs differ by the same amount.
200
For h(x) = 3x +2
What is the x value when h(x) = -7?
x = -3
200
What is the slope of the line through the 2 points
(-1, 3) and (4, -2)?
m = -1
200
Describe the transformation done to the function.
(vertical or horizontal or flip? Left, right, up, down, flip over x-axis or flip over y-axis?)
f(x)= x + 5
g(x)= -f(x)
Flip over the x axis.
300
What is the domain and range of the following function?
(-2, 5), (0, 2), (1, 1), (5, -3), (7, -2)
Domain?
Range?
Domain: {-2, 0, 1, 5, 7}
Range: {5, 2, 1, -3, -2}
300
Does the equation represent a linear function? Explain.
y = 2x2 - 7
NO. The equation is not in y = mx + b form.
300
What is the x value when f(x) = 7?
x = 5
300
What is the slope and the y intercept for the following equation?
2x - y = -6
m = 2
b = 6
300
Which does not belong?
(0,-3) (0,0) (4,-3) (4,0)
(4,-3)
400
What is the domain and range of the following function?
Domain? Range?
Domain is -2 < or = x < or = 3
Range is -1 < or = y < = 2
400
Is the domain discrete or continuous? Explain.
Discrete. Whole numbers, countable.
400
What is f(x) when x = 2?
f(x) = 2
400
Graph the equation:
2y = -4x +6
Put a point on the y axis at positive 3, and from that point, go down 2 and right 1 and put another dot.
400
Describe the transformation of f(x).
f(x) = -3x -1
g(x) = f(x-2)
Horizontal movement, 2 to the right
500
If the function g(h) stands for the grade you earn based upon the number of hours, h, you study in a week, explain the following.
g(1) < g(9)
The grade you earn from studying one hour a week is less than the grade you earn from studying nine hours a week.
500
What is the domain? Is it discrete or continuous?
Domain is [0, 4]. It is discrete.
500
The function d(t) = 300,000t represents the distance in kilometers that light travels in t seconds.
How long does it take light to travel 12 million kilometers?
40 seconds
500
What is the equation of the line if the dependent variable increases by 3 when the independent variable decreases by 1 and the point (0, 2) is on the graph?
y = -3x + 2
500
Will the graph of the transformation be skinnier or fatter? Explain.
f(x) = absolute value of (x + 2)
g(x) = 1/2 absolute value of (x + 2)
Fatter. The function is being multiplied by a number between 0 and 1, or a is a fraction.