Lines
Find the slope of the line passing through the two points.
(7,-1), (8,2)
The slope is 3.
Is the set of ordered pairs a function from set A to set B?
A = {10, 20, 30, 40} B = {0, 2, 4, 6}
{(20,4), (40,0), (20,6), (30,2)}
It is not a function because element 20 in A corresponds to two elements, 4 and 6, in B.
Find the domain and range of f(x)=3-2x2.
D: all real numbers x
R: (-infinity,3]
f(x)=3-2x
g(x)=sqrt(x)
Find (g composed of f)(-3)
3
Determine whether the points are positively correlated, negatively correlated, or have no discernible correlation.
See board.
No correlation.
Find the equation of the line that has a slope of 1/4 and goes through the point (2,-1).
y = 1/4 x - 3/2
Determine whether 16x2 - y2 =0 represents y as a function of x.
Not a function.
Use the Vertical Line Test to determine whether y is a function of x of y-4x=x2.
Use a graphing calculator.
Function.
Find two functions such that (f composed of g)(x)=h(x)
h(x)=(x+3)2
f(x)=x2
g(x)=x+3
(75, 2.3), (82, 3.0), (90, 3.6), (65, 2.0), (70, 2.1), (88, 3.5), (93, 3.9), (69, 2.0), (80, 2.8), (85, 3.3)
Does the relationship between x and y appear to be approximately linear?
Yes
Find the equation of the line that passes through these two points:
(-1,0)
(6,2)
y = 2/7 x + 2/7
Evaluate the function f(x) = x2+1 at f(x -1).
f(x - 1) = x2 - 2x + 2
Use a graphing utility to determine behavior of the function at certain intervals.
*hint* use increasing, decreasing, or constant
f(x)=x3-3x
Increasing on (-infinity,-1), (1, infinity)
Decreasing on (-1,1)
Find the inverse of f(x)=6x.
f-1(x)=x/6
(4, 4.203), (8, 4.150), (12, 4.005), (16, 3.866), (20, 3.855), (24, 3.854), (28, 3.783), (32, 3.750), (36, 3.800), (40, 3.677), (44, 3.718), (48, 3.698)
Use the regression feature of a graphing utility to find a linear model for the data.
y=-0.0109x+4.146
Write the slope-intercept form of the equation of the line that goes through (3,-2) and is parallel to 5x-4y=8.
y = 5/4 x - 23/4
Find the domain of x-1/x+2.
All real numbers except -2
Identify the parent function and the transformations of the h(x)=-(x-2)3+5
f(x)=x3
horizontal shift two units right
vertical shift five units upward
reflection in the x-axis
Use a graphing utility to graph and use the Horizontal Line Test to determine whether f(x) = 1/2 x - 3 is one-to-one and an inverse exists.
One-to-one
(4, 4.203), (8, 4.150), (12, 4.005), (16, 3.866), (20, 3.855), (24, 3.854), (28, 3.783), (32, 3.750), (36, 3.800), (40, 3.677), (44, 3.718), (48, 3.698)
Is the model (line of best fit) a good fit for the data.
Yes
Write the slope-intercept form of the equation of the line that goes through (-8,3) and is perpendicular to 2x+3y=5.
y = 3/2 x + 15
Find the difference quotient f(x+h)-f(x)/h for f(x)=2x2+3x-1.
2h+4x+3, h cannot equal 0
Determine whether the function is even, odd, or neither.
f(x)=x2+6
Even
Find the inverse of
f(x) = 1/4 x2 + 1, x is greater than or equal to 0
f-1(x)=sqrt(4x-4)
(4, 4.203), (8, 4.150), (12, 4.005), (16, 3.866), (20, 3.855), (24, 3.854), (28, 3.783), (32, 3.750), (36, 3.800), (40, 3.677), (44, 3.718), (48, 3.698)
Create a scatter plot.
See board