Functions and Graphs
Identify the y-int and x-int, then graph.
y = 2x - 3
y-int= (0, -3)
x-int= (1.5, 0)
A function f is given by f(x) = 3x + 2
Find f(3), f(-1), and f(1/2)
f(3)= 11
f(-1)= -4
f(1/2)= 7/2
False; domain is the set of all x values, range is the set of all y values
How do you find the slope of a line?
m = (y2- y1) / (x2- x1)
What do we use to determine if something is a function?
the Vertical Line Test
Identify the y-int and x-int, then graph.
y= x^2 +2
y-int= (0, 2)
no x-int
A function f is given by f(x) = x^2 - 5
Find f(4), f(-2), and f(1/2)
f(4)= 11
f(-2)= -1
f(1/2)= -19/4
Determine the domain and range from the ordered pairs
f= { (-3, 1), (-2, 5), (1, -2), (3, 0), (4, 5) }
D: {-3, -2, 1, 3, 4}
R: {-2, 0, 1, 5}
Find the slope of a line containing the points (-2, 6) and (-4, 9)
m = -3/2
T/F: This is an example of a function
{ (2, 5), (4, -6), (3, 5), (2, -6) }
False
Identify the y-int and x-int, then graph.
y = 5
horizontal line going through (0, 5)
A function f is given by f(x) = -x^3 + 3
Find f(2), f(-2), and f(2a)
f(2)= -5
f(-2)= 11
f(2a)= -8a^3 + 3
Find the domain and range of f(x) = 3x + 2
D: all real numbers (-inf, inf)
R: all real numbers (-inf, inf)
a) What is the slope of y= 4?
b) What is the slope of x= -3?
a) m= 0
b) undefined
Solve 2x^2 - 14x + 24 = 0
x = 3, 4
Identify the y-int and x-int, then graph.
y - 8 = x^3
y-int= (0, 8)
x-int= (-2, 0)
A function f is given by f(x) = x^2 + 4
Find f(2x+h) - f(0)
4x^2 + 4xh + h^2
Find the domain of f(x) = 3 / 2x - 5 and write it in interval notation
D: (-inf, 5/2) U (5/2, inf)
y = 2x - 3
x^2 - 6x + 8
Identify the y-int and x-int, then graph.
y + 1 = -x^3
y-int= (0, -1)
x-int= (-1, 0)
A function f is given by f(x) = x^2 + 4
Find [f(x+h) - f(x)] / h
2x + h
Find the domain of f(x)= (5 + 3x)^1/2 and write it in interval notation
D: [ -5/3, inf)
Find the equation of a line containing the points (-1, 4) and (3, -6).
y = -5/2x + 5/2
Determine if f(x) = x^3 + 1 is even, odd, or neither
Neither