1.4 A- Function Notation & Evaluating
A function is defined as: inputs can have 2 or more outputs. Explain why
True or False
What is False?
Every input has exactly 1 output.
Solve the operation:
f(x) =2x +1
g(x)= x2 - 9
f(2) + g(-1) =
What is ...
f(2) + g(-1) = -3
Find the inverse function for:
f(x)= x2 + 5
What is f-1(x) = sqrt(x-5) ?
Another term for saying the domain is from
(-infinity, infinity)?
What is "All Real Numbers"?
Evaluate the piecewise function:
f(x) = { x+2 x<0
-x - 4 x>= 0
F(-2)=
F(-2)= 0
Is this a function? Explain why
{ (3,4), (4,5), (6,7), (3,9) }
What is no?
Input "3" has 2 different outputs.
Solve the operation:
A(x) = x2 + 5
B(x) = square root of x
(A * B)(16) =
What is ...
(A * B)(16) = 1,044
Are the following inverses?
f(x) = 7x -1
f-1(x) = (x+1)/7
What is yes? Proven by plugging inverse into OG function and you get the input "x".
The end behavior for this function:
f(x) = -x3 + x2 -3
What is...
Odd
Negative
x --> Negative Infinity f(x) --> Positive infinity
x --> Positive infinity f(x) --> Negative Infinity
Evaluate:
h(x) = { x3 -2x +7 x<= -1
| x2 - 8 | -1 < x < 2
x2 -5x -6 x >= 2
h(0)=
What is h(0) = 8?
What is the domain and range of the function?
{ (3,90), (4,54), (6,71), (8,90) }
Range = {54, 71, 90}
Solve the composition:
f(x) = x2 - 4x - 1
g(x) = 3x2 - 6
find f(g(-2))
What is f(g(-2)) = 11?
Name the 8 parent functions and list their respective equation.
Linear - f(x) =x
Quadratic- f(x) =x2
Cubic- f(x) =x3
Absolute Value- f(x) =|x|
Square Root- f(x) =sqrt (x)
Rational- f(x) = 1/x
Exponential- f(x) =2x
Logarithmic- f(x) =log(x)
What is an x-intercept and a y-intercept?
What is...
x-intercept- where the function crosses/touches the x-axis
y-intercept- where the function crosses/touches the y-intercept
Evaluate:
h(x) = { x3 -2x +7 x<= -1
| x2 - 8 | -1 < x < 2
x2 -5x -6 x >= 2
h(-1)=
What is h(-1) = 8 ?
Solve the following: F(-3)
F(x) = 2x2 - 3x + 9
What is F(-3) = 36
Solve the composition:
f (x) = x2 + 5
g(x) = 3x +11
Find: (g o f)(n)=
What is (g o f)(n)= 3x2 + 26 ?
List the transformations here
f(x) = -(x+3)2 -5
What is down 5, left 3 and flip over the x-axis?
What is the difference between relative and absolute extrema? And can your extrema include infinity?
What is... Relative extrema refers to maximum or minimum points on a curve within a specific interval, while absolute extrema represent the overall highest and lowest points on the entire curve or domain. ?
Graph the piecewise function:
f(x) = { x + 5 x<-2
-4 x>= -4
Graph on paper
A local plumber charges a flat service fee of $75 for a house call plus an hourly rate of $45 per hour. Write a function to represent the situation, then find f(3) and explain what it means in the context of the problem.
What is ...
f(x) = 45x+75
f(3)= 210
$210 it will cost for a plumber for 3 hours of work
PJ has met all of his sales goals at his job and his company is rewarding him with a bonus and a salary increase. PJ’s base salary is $52,000. His company is going to give him a 3% increase in salary and then a $2,000 bonus after. What will PJ’s salary be after both changes are made?
What is a salary of $55,560?
Write the new function after this transformation:
Cubic- translated 7 units up, 4 units to the right and flip over y-axis
What is
F(x) = (-x - 4)3 +7
Graph the following:
Infinite
Domain: (-∞, ∞)
Range: (-∞, 3]
End Behavior : Even/Negative
Increasing: (-∞, 3) and (2,5)
Decreasing: (3,2) and (5, ∞)
Relative Min: None
Relative Max: x= 3
y- intercept : (0,0)
x- intercept (zeroes): (-5,0), (0,0),
(4,0) and (6,0)
Graphs on paper
A t-shirt company sells t-shirts for $12 apiece if you buy 10 or less. If you are willing to buy between 11 and 50, they will cut you a deal and sell them to you for $10 apiece. If you are willing to buy more than 50, they will sell them to you for $8 apiece.
1) Create your piecewise function.
2) Evaluate for f(70) =
What is ...
f(x) = { 12x 0< x=< 10
10x 11=< x =< 50
8x x > 50
f(70)= $560