Defining Relations and Functions
What graphical test is used to determine if a graphed relation is a function?
Vertical Line Test
If f(x)=3x−5, find the value of f(4).
7
Does the equation y = 3x2 − 4 represent a linear or non-linear function?
Non-linear
What is the domain of the relation
{(1,5),(2,10),(3,15)}
Needs to be in order!
{1,2,3}
Find the y-intercept of the function f(x)=−2x+7.
7 or (0,7)
TRUE OR FALSE
The relation {(1,2),(2,3),(1,4)} is a function
FALSE
The input 1 maps into two outputs
If g(x)=−2x+8, find the value of g(−3).
14
What is the constant rate of change (slope) of the linear function f(x)=−5x+12?
-5
For the real-valued function f(x)=x, explain why the domain cannot include negative numbers.
Because the square root of a negative number is not a real number.
Find the x-intercept of the function f(x)=3x−9
(3,0) or 3
TRUE OR FALSE
For the given scenario, it displays a continuous relation:
The population changes of your school over the past 5 years
FALSE
You cannot connect the dots on this graph since you cannot have half a person
If f(x)=2x + 3 and f(x)=9, find the value of x.
3
Does the following table represent a linear function?
x: [1, 2, 3, 4]
y: [3, 7, 11, 15]
YOU NEED TO EXPLAIN WHY TO RECEIVE POINTS!
YES
There is a constant rate of change (first difference) of +4 for every increase of 1 in x.
Slope (m) = 4/1 or 4
A graphed line segment starts at [−2,1] and ends at [4,5], with both endpoints included.
State the range of this relation in interval notation.
[1,5]
If a graph of a function f(x) has a y-intercept at (0,−4), what is the value of f(0)?
-4
TRUE OR FALSE
Given a mapping diagram where Set A {2,4,6} maps to Set B {5,10}, such that 2→5, 4→10, and 6→5 is a function
TRUE
Every input in Set A maps to exactly one output in Set B.
If f(x)=4x−7 and f(x)=13, find the value of x.
5
Find the constant rate of change for the linear function that passes through the coordinates (2,5) and (4,11).
Simplify if possible.
3 or 3/1
A graphed line segment starts at (3,-1) and ends at (6,2), with both endpoints not included.
State the domain of this relation in set notation.
{x | 3 < x < 6, xER}
A linear function has an x-intercept of (3,0) and a y-intercept of (0,−6). Write the equation of this function in f(x)=mx+b form.
f(x)=2x−6
TRUE OR FALSE
For the relation defined by the equation x=y^(2), y is NOT a function of x.
TRUE
If x=4, then y can equal both 2 and −2 (since 22=4 and (−2)2=4). One input maps to two outputs.
Given h(x)=x2 −2x +5, find the value of h(−2).
13
A cell phone plan charges a flat monthly fee of $20 plus $0.10 per text message sent. Write a function C(t) to represent the total monthly cost for t texts.
C(t)=0.10t + 20
Given the endpoints (-4,9] and [2,3), give the range in set notation
Beware of the types of brackets given.
{ y | 3 < y <-- 9, yER}
A linear function passes through points A(6,3) and B(4,5). Write the equation of this function in f(x)=mx+b form.
f(x) = -x + 9