Function Fun
What is the parent function for all linear functions?
f(x)=x
A table shows the relationship between hours worked and money earned. Is this a visual representation of the data?
No, it's a numerical representation. A graph would be a visual representation
The price of a concert ticket is $25. What is the equation for the total cost, C, if you buy T tickets?
C=25T
The graph of y=2x+4 crosses the y-axis at what point?
(0, 4)
The graph of y=x^2+5 is a shift of the parent function. What is the direction and magnitude of the shift?
5 units up
The parent function is f(x)=x . If the new function is g(x)=x+3 , what is the new output if the input is x=2 ?
g(2)=2+3=5
A word problem says, "A taxi charges a flat fee of $5 plus $2 per mile." Write an equation to represent this situation.
C=2m+5 (or something similar, where C is cost and m is miles).
A car gets 20 miles per gallon. Write an equation showing the distance traveled (D) as a function of gallons used (g).
D=20g
The equation y=3x-6 is a line. What is its x-intercept?
(2, 0)
You have a table showing hours worked and money earned. The numbers are:
(1, 15), (2, 30), (3, 45)
Write a verbal description of this relationship.
For every hour worked, you earn $15.
A function is transformed to become g(x)=-|x| . If the original output for x=5 was 5, what is the new output for x=5 ?
g(5)=-|5|=-5
A graph shows a straight line passing through the points (0,4) and (2,8) .Write a verbal description of this relationship.
It starts at a value of 4 and increases by 2 for every 1 unit increase in the x-value.
A phone plan costs $40 per month plus an extra $10 for every gigabyte of data you use over your limit. What's the cost for a month where you use 3 extra gigabytes?
$40 + 10(3) = $70
A student is selling t-shirts. The profit is represented by the equation P(n)=15n-100 , where n is the number of t-shirts sold. How many t-shirts must they sell to break even (make $0 profit)?
7 t-shirts. (Since 15n-100=0 -> 15n=100->n=6.67 . They must sell the 7th shirt to break even).
What is the parent function for all absolute value functions?
f(x)=|x|
The parent function is f(x)=x^2 . The new function is g(x)=x^2-1 . If the original output for x=4 was 16 , what is the new output for x=4 ?
g(4)=4^2 −1=16−1=15.
Given the equation y=x^2-1 , create a simple table of values for x={-1, 0, 1} .
x | y
-1 | 0
0 | -1
1 | 0
Your savings account starts with $50. You add $10 every week. Create a table of values for the first 3 weeks.
WEEK | SAVINGS
0 | $50
1 | $60
2 | $70
3 | $80
Look at this graph (present a graph of a line, e.g., passing through (0, 5) and (10, 0) ). What is the equation of this line in slope-intercept form?
y=-0.5x+5
Create a word problem that could be solved by the equation y=50+10x .
Answers will vary.
Example: "You have a $50 gift card and you get $10 for every chore you do. What is the total amount of money you have if you do x chores?"
The graph of f(x)=sqrtx is stretched vertically by a factor of 3.
What is the new function's equation?
What is the new output for an input of x=9 ?
New Equation: g(x)=3sqrtx
New Output: g(9)=3sqrt9=3(3)=9
Draw a graph that represents the equation y=-x^2 What is the name of this type of graph?
The student should sketch a downward-facing parabola with its vertex at the origin. The name of the graph is a parabola.
A graph shows a linear relationship where a line passes through (0, 100) and has a slope of -5 . What's a real-world scenario that could be represented by this graph?
Answer should describe something (ex. 100g water tank) that starts at a value of 100 and decreases by 5 units for every 1 unit of time/increase.
The graph of f(x)=sqrt(x+4) has what domain and range?
Domain: x >=-4
Range: y>=0
A graph of an exponential function passes through the points (0, 1) and (1, 3) . The graph of this function is shifted 2 units down. Write the new equation.
The original function is y=3^x . The new function is y=3^x-2 .