Am I a function?
Algebra of Functions
To Infinity & Beyond
Domain & Range
Quads
Graph props.
blah blah blah
f(Lpz)
1
The function classification of this graph and explanation for it
What is NOT a function and because it has two outputs for at least one input ( fails vertical line test) ?
1
Determine algebraically if the following function is Even, Odd, or Neither
f(x)= sqrt(x-5) +2
What is Neither?
f(-x) is invalid so Even and Odd test failt
1
Sketch a graph that satisfies the condition and name it
Various answers work, for example:
1
Find Domain and range:
R: yge-1 or [-1, infty)
D:[-2,infty)
1
Given the graph of r(x) below, find the vertex form, standard form and factored form.
What is:
VF: r(x)=(x-3)^2-1
SF: r(x)=x^2-6x+8
FF: r(x)= (x-2)(x-4) ?
1
Domain and Range of the graph
What is
D: (-infty, infty)
R: [-1, infty) ?
1
The meaning of
f, f(x), and x
What is
f: function name
f(x): output value
x: input value ?
1
What place in Mexico is Lopez from?
What is Oaxaca?
2
The function classification of the relation f mapping set A to set B and the domain, range, and codomain
What is Yes, it is a Function? And what are
D:\{a_1, a_2, a_3,a_4\}, R: \{b_1, b_3, b_4\}, CD: \{b_1,b_2,b_3,b_4,b_5\}?
2
Determine algebraically if the following function is Even, Odd, or neither:
g(x) = {6x^3}/{7-x^4}
What is Odd?
g(x)={6x^3}/{7-x^4}
g(-x)= {6(-x)^3}/{7-(-x)^4}={-6x^3}/{7-x^4}= -{6x^3}/{7-x^4}
therefore g(x) = - g(-x)
2
Sketch two graphs that satisfy the conditions listed below and name them:
multiple examples work, here are two:
2
Find Domain, Range
D:(infty,-1)cup(-1,1)cup(1,infty)
2
Given the graph of s(x) below, find the vertex form, standard form and factored form.
What is:
VF: s(x)=-(1)/(2) (x-4)^(2)+2
SF: -1/2x^2+4x-6
FF: s(x)=-\frac{1}{2}(x-2)(x-6)
2
The increasing and decreasing intervals of f(x)
What is
Inc: (-1, 0) cup (1, infty)
and
Dec: (-infty, -1) cup (0,1) ?
2
The meaning of an even function and the meaning of an odd function. Also provide the tests we do for them
What is
even: sym abt y-axis, f(x)=f(-x)
odd: sym abt origin, f(x)= -f(-x)
?
2
What did Lopez do right after Covid?
What is skydive?
3
The ones that aren't functions explain why specifically?
What is A & B are functions because every input has only one output? And also C fails because the input 0 has two different outputs and D fails because the input of a has two different outputs?
3
Determine algebraically if the following function is Even, Odd, or Neither:
h(x) = x^2-x
What is NO, this is Neither?
3
What is the end behavior
xto-infty, f(x) to2
xtoinfty, f(x) to2
3
The domain and range of the graph below
D:(-infty,1)cup(1,infty)
R:(-infty,3)cup(3,infty)
3
A soccer player kicks a ball into the air from a height of 2 feet. The ball leaves the player's foot with an initial upward velocity of 48 feet per second. The height of the ball, hhh, after ttt seconds is modeled by
h(t)=−16t2+48t+2.h(t)=-16t^2+48t+2.h(t)=−16t2+48t+2.
(A)
After how many seconds does the ball reach its maximum height?
(B)
What is the maximum height of the ball?
What is:
t=1.5 seconds
max height: 38 feet
3
The extrema (max/min) given as points and type (relative/absolute) of f(x)
What is
Local Max @ (0,0) and
Absolute Mins @ (-1, -1), (1, -1) ?
3
The name of the highest or lowest point on a parabola and the equation we use to solve for the x-value of it
What is the vertex? and what is
{-b}/{2a}?
3
Where did Lopez go last summer and which artist did he catch in concert there?
What is Puerto Rico and Bad Bunny?
4
What is, No the student is not correct?
The pairs are identical, the repeated input has the same output so it's the exact same point written twice
4
Determine algebraically if the following function is Even, Odd, or neither:
w(x) = x^2-1
What is Even?
4
The end behavior of the graph below
What is
xto-infty, f(x) to3
xtoinfty, f(x) to3
4
Find the function (g/f)(x) and it's domain.
What is (g/f)(x)=6/{(x+3)sqrt(5-x)} and
(-infty,-3) cup (-3,5)?
4
At a Fourth of July celebration, a firework is launched from a platform 6 feet above the ground. It rises with an initial velocity of 64 feet per second. The height of the firework, hhh, after ttt seconds is modeled by
h(t)=−16t2+64t+6.h(t)=-16t^2+64t+6.h(t)=−16t2+64t+6.
(A)
After how many seconds does the firework reach its maximum height?
(B)
What is the maximum height of the firework?
What is
t= 2 seconds
max height = 70 feet
4
The x and y intercepts written as points for f(x)
What is
y-"int": (0,0)
x-"int": (- sqrt(2), 0), (0,0), (sqrt2, 0) ?
4
The problem "areas" for domain we have dealt with so far and how do we tackle them
What is the denominator of a fraction (set them equal to 0 so we can remove that input from our domain) and square root (we set everything under sqrt to ge0 because we can't have negative under square root?
4
What did Lopez do this 4th of July?
What is catch fireworks from the sky on a small plane?
5
Select the best answer and Explain why it's true and write the final list of points inside {}
What is option C?
Because the input 4 cannot have more than one output so a must equal 5 meaning the point just got repeated... b,c ne 4 because that would lead to the input of 4 having more than one output.
5
Find the x and y intercepts of the following function (as points):
f(x)= x^5-8x^2
What is x-int: (0,0), (2,0) and y-int: (0,0)?
5
f(x) = 2x^2 + 12x + 16
What is the average rate of change of f(x) on the interval [-3, -2].
2
5
Find
(f/g)(x) and (g/f)(x) and provide their domains.
What is:
(g/f)(x)={x+4}/{(x-2)sqrt(x-1)}
D: (1,2) cup(2,infty)
(f/g)(x)={(x-2)sqrt(x-1)}/{x+4}
D:
5
Factor the following:
What is?
5
The average rate of change of f from x=-1 to x=0
and the average rate of change from x=0 to x=1. (setup matters)
What is
{f(0)-f(-1)}/{0-1}={0-(-1)}/{-1}= 1
{f(1)-f(0)}/{1-0}={-1-0}/{1}= -1 ?
5
The form that the x intercept will always have and the form that the y intercept will always have.
Also the way we solve for both of them
What is (x,0) for x-int and (0,y) for y-int (0,y)?
What is set f(x)=0 and solve for the x value for x-int?
And what is set x=o and find out what f(0) gives us for the y-int?
5
How many Ping Pong Championships did Lopez win at Fresno State?
What is 7?