Show:
Writing Functions
Recursive, Inverse
Domain, Range
Comparing Functions
Mix
100
Jakhyra has scored 35 points this season and is scoring 7 points each quarter. How many points does she have at the 3rd quarter?
f(x) = 7x + 35 f(3) = 7(3) + 35 f(3) = 56 56 points
100
Write a recursive function for the sequence 1, 3, 5, 7, 9....
a1 = 1 an = an-1 + 2
100
What is the range for the function g(x) = -2x + 7 if the domain is {2, 3, 4}
{3, 1, -1}
100
Which has a steeper slope? f(x) = 3x + 10 4x + y = 10
The first, f(x), has a slope of 3. The second must be turned into slope intercept form: y = -4x + 10, has a slope of -4. The first has a steeper slope!
100
What is a "line of best fit" and why is it useful?
A line of best fit is drawn on a scatterplot to model the relationship. It's a linear function drawn on data that is NOT a function.
200
Ms. Parquette has $100. She buys some hot chocolate packets ($1 each) and some basketballs ($5 each). Write an equation showing how many hot chocolate packets and how many basketballs she can buy for $100.
x + 5y = 100 (Can use any variables here, but your equation should be in standard form!)
200
Write an explicit function for the recursive function: a1 = 5, an = an-1 +10
y = 10x - 5
200
Define domain
The inputs (or x-values) in a function.
200
Which has a smaller y-intercept? x + y = 100 (y - 80) = 2(x + 50)
The first one has a y-intercept of 100 (y = -x + 100) The second one has a y-intercept of 180 (y = 2x + 180) The first one has a smaller y-intercept!
200
What is a piecewise function and why is it useful?
A piecewise function is a function that has more than one part. You draw the function and then use the domain to decide which part of the function to keep.
300
Write an equation that has an x-intercept of 7.5 and a slope of 2/3.
Point-slope form is easiest here! x-intercept means there is a point at (7.5, 0) y - 0 = 2/3(x - 7.5) OR y = 2/3x - 5
300
Write an inverse function for f(x) = 3x - 2
f'(x) = 1/3x + 2/3
300
Define range.
The outputs (or y-values) of a function.
300
Write an equation that has a steeper slope than y = -1x + 5,000,000
Any equation with a slope that is greater than -1. (It doesn't matter what the y-intercept is!)
300
Draw a picture of the function y = -2/3 x + 5
The y-intercept should be 5. The slope says, "go down 2, go to the right 3". You should have arrows on each end of the line.
400
Write an equation for a line that is perpendicular to y = 3x + 10 and goes through the point (2, 3).
perpendicular = slope is opposite reciprocal = -1/3 point slope answer: y - 3 = -1/3(x - 2) slope-intecept answer: y = -1/3x +3 2/3
400
What is the 3rd term in the sequence a1 = 10, an = an-1 + 12
10, 22, 34 The third term is 34!
400
What is the domain and range of the function h(x) = 1/2x + 100, which shows the temperature x minutes after a stove is turned on.
domain: All positive numbers range: h(x) >_ 100
400
Write a function that is undefined.
Any equation that would make a vertical line (e.g. x = 3)
400
How many solutions do you see in a line with an arrow at each end?
Infinite solutions!
500
John is mowing lawns. He pays $350 for a lawn mower and then earns $20 per lawn mowed. He writes the following equation g(x) = 20x - 350 to find his profit. Is (100.5, 1660) a solution? Why or why not?
It's a solution to the equation but NOT a solution in this context, because you can't mow 1/2 a lawn. The domain is whole numbers, so 100.5 is NOT in the domain.
500
Write the inverse of g(x) = x + 10 and then find the 4th term.
g'(x) = x - 10 -9, -8, -7, -6 -6 is the 4th term!
500
The function, 4x + 2y = 20, shows the combinations of apples (x) and bananas (y) you can buy for $20. What is the domain and range of this function?
Domain = number of apples, 0 to 5, whole numbers Range = number of bananas, 0 to 10, whole numbers (You need to find the x and y-intercepts to solve this problem!)
500
Write the equation for a line that has a slope of zero.
Any equation with a horizontal line. For example: y = 0x + 5 y = 5 (These are the same lines!)
500
What is the difference between an arithmetic and a geometric sequence?
Arithmetic = repeated additon = linear Geometric = repeated multiplication = exponential