Distance and Midpoint Formulas
What is the distance formula between two points (x1, y1) and (x2, y2)?
sqrt((x2-x1)2+(y2-y1)2)
What is the domain of the relation given by the set of points ((1,2), (3,4), (5,6))
Domain = {1,3,5}
What are intercepts on a graph?
The places where the graph cross either the x or y axis
What does it mean to translate a function?
The graph will either be shifted it up, down, left or right
What is an inverse function?
The reflection of a function across the line y=x.
The function that undoes the operations of the original function.
How do you find the midpoint of a line segment?
0.5(x1+x2), 0.5(y1+y2)
Identify its domain and range given the function f(x) = x2 - 3.
Domain: All real numbers
Range: [-3, oo)
How do you find the y-intercept of the equation y = 3x + 2?
The y-intercept is the b value in the equation y=mx+b. So the y-intercept would be 2.
Describe how to perform a vertical shift on the standard quadratic function f(x) = x2.
Add/Subtract a value to the end of the function
How do you find the inverse of a function algebraically?
Step 2: Solve for y
Find the distance between the points (1, 2) and (4, 6)
5
Identify the slope and y-intercept of the equation (2y = 4x + 8).
Slope: 2
Y-int: 4
Given the graph of a function, how can you identify its slope?
The slope is rise over run or can be calculated by taking y2-y1 divided by x2-x1
How do you perform a transformation on the absolute value function?
Adding/subtracting values will cause translations
Multiplying values will cause stretch/compressions
Multiplying by negative will cause reflection
Given the function f(x) = 2x + 3, find its inverse.
Calculate the midpoint of the segment connecting (2, 3) and (4, 7)
(3,5)
Does the equation y = x2 + 4 represent a function? Explain why or why not.
Yes, it will pass the vertical line test
Describe how to graph a horizontal line and provide an example.
All y values remain the same no matter what x value is selected.
y=#
Explain how to reflect a function over the x-axis.
Multiply the function by -1, -f(x)
Given the function f(x) = sqrt{x + 1}, find its inverse
f-1(x)=x2-1
What do h and k stand for in the equation (x-h)2+(y-k)2=r2
r is the radius
What is its domain and range if the relation is defined by the equation y = sqrt{x - 1}?
Domain: [1,oo)
Range: [0,oo)
Given the graph of a function, how would you identify the domain and range?
Domain represents all possible x values shown
Range represents all possible y values shown
Given the function f(x) = (x - 2)2 + 3, describe the transformations applied to the parent function f(x) = x2.
Shift right by 2, up by 3
What is the significance of the horizontal line test in determining if a function has an inverse?
If the function does not pass the horizontal line test, that indicates the "inverse" may contain undefined pieces