Evaluating Functions
f(x)=x-5
Find f(8).
f(8)=3
Yes. Each x-value (input) has exactly one y-value (output).
The number of students in each class period: continuous, discrete or neither? Explain.
Discrete. You count whole students.
Is y=2x+7 linear or nonlinear? Explain.
Linear. Its graph is a straight line.
The number of goals a soccer team scores in each game.
Discrete. Goals are whole numbers, so there are no values in between.
g(x)=-4x+11
Find g(4).
g(4)=-5
Is {(1,5), (2,6), (1,7)} a function? Explain.
No. The input 1 goes to both 5 and 7.
A plant's height as it grows over the day: continuous, discrete, or neither? Explain.
Continuous. Height has a value at every moment.
Is y=-4x linear or nonlinear?
Linear. The line goes through the origin with a slope of -4.
Yes, the repeated output and repeated ordered pair is okay! Each input still has only one output.
f(x)=2x2-3x+4
Find f(3).
f(3)=13
A vertical line that passes through the graphed function at 2 points.
Not a function.
A water tank fills a tank at a steady rate. x=minutes, y=gallons. Continuous, discrete, or neither? Explain.
Continuous, the tank has a measurement of water at each moment in time.
Nonlinear. The x2 term makes the function a u-shape (parabola), which is not a straight line.
h(x)=x2-5, find h(-3).
h(-3)=4
h(x)=7x-8
Find h(6)+9.
h(6)+9=43
Table: x=0,1,2,3 and y=4,4,4,4. Is this a function? Explain.
Yes, repeated outputs are okay! Each input has only one output.
Carl is buying movie tickets for his friends. Each ticket costs $9.00. He graphs the tickets on the x-axis and total cost on the y-axis. Would this graph be continuous, discrete, or neither? Explain.
Discrete. Carl can only buy a whole number of tickets, so the graph would be separate dots and should not be connected.
Given the ordered pairs, determine if the function is linear. Explain.
(0,6)
(2,12)
(4, 18)
(6, 24)
Yes, the x-values and the y-values both go up at constant rates of change.
f(x)=x+6 and g(x)=2x-1.
Find f(4) - g(3).
f(4)-g(3)=5
f(x)=x2-x+3
Find f(2)+f(-3).
f(2)+f(-3)=20
The input is each person in this class, and the output is their birthday. Is this a function?
Yes, every person has one birthday.
A parking garage charges the following:
0 to 1 hour: $3.00
More than 1 hour up to 2 hours: $6.00
More than 2 hours up to 3 hours: $9.00
More than 3 hours: $12.00
Is this Continuous, Discrete, or Neither? Explain.
Neither, this function is in groups, or chunks.
Determine if the function is linear or not. Explain your answer.
f(x)= 2(x+3)2-5
No, because simplifying will show us that there is an x2 term that makes the function a u-shape, so it is not linear.
Is the function linear or not?
f(x)=x(2+4)2-7
Yes it is linear. When you simplify the equation, you do not get an x2 term, or anything else that makes it nonlinear. (f(x)=36x-7)