Basic Functions and Their Graphs
What is the domain of the relation {(1,2), (3,4), (9, 2), (6, 7)}
Domain: {1, 3, 9, 6}
Is the identify function f(x)= x, even, odd or neither
f(x)=x is an odd function because it is symmetrical to the origin.
What is the slope- intercept form of the line passing through (-1, 5) with x-intercept -4.
y=5/3x+20/3
What is the name of the function f(x)=x²
the Quadratic function
Is the function {(1, 2), (3, 4), (6, 5), (8, 5)}
Yes, no x value is repeated so it is a function.
If the function f(x)={x-3 if x<0
{x-2 if x>0
What is f(8)?
f(8)= 6
Give the slope and y-intercept of 6x-12=0
slope= undefined
no y intercept
What transformation occurs when f(x)+c
Move up c units
If f(x)= x²-2x+7, evaluate f(-5).
f(-5)= 42
What is the difference quotient for x²-2x
2x+h-2
Find the x and y intercept of 4x-y=4
x- intercept= 1
y- intercept= -4
What transformation occurs when f(x-c)
move to the right c units
What is the domain and range for f(x)= |x|
Domain: (-inf, inf)
Range: (0, inf)
Determine whether f(x)=3x²-5x is even or odd or neither.
Neither because f(-x)=3x²+5x
John has purchased four pounds of rice from the market for $20. What is the cost for 1 pound of rice?
one pound of rice is $5
Name the parent function and explain the transformation for f(x)= -(x+1)²-3
Quadratic Function
-f(x); reflect about the x axis
-f(x+1); Move to the left 1 unit
-f(x+1)-3; Move down 3 units
What are the x and y intercepts of 3x-4y=12
x- intercept: (4, 0)
y- intercept: (0, -3)
Let the function M(t)=15t represent the distance you would travel by bicycling t hours. Assume you can bike no more than 10 hours, determine he practical domain for the function.
Domain: [0, 10]
The domain t is the amount of reasonable hours since you cant bike more than 10 hours [0, 10] and hours cannot be a negative value.
Mike and Sarah collect rocks. Together they collected 50 rocks. Mike collected 10 more rocks than Sarah. How many rocks did they each collect.
m+s=50
m=10+s
(10+s)+s=50
s=20
m=30
Name the parent function and graph transformations that occur for f(x)=3|-½x+8|+12
Absolute value function
Vertical Stretch by a factor of 3
Reflection over the y-axis
Move to the left 8 units
Move up 12 units