Precalculus : Functions
Study concepts, example questions & explanations for Precalculus
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Example Questions
Example Question #1 : Determine If A Relation Is A Function
Which of the following expressions is not a function?
Recall that an expression is only a function if it passes the vertical line test. Test this by graphing each function and looking for one which fails the vertical line test. (The vertical line test consists of drawing a vertical line through the graph of an expression. If the vertical line crosses the graph of the expression more than once, the expression is not a function.)
Functions can only have one y value for every x value. The only choice that reflects this is:
Example Question #2 : Determine If A Relation Is A Function
Suppose we have the relation 
The relation is a function because every relation is a function, since that's how relations are defined.
The relation is not a function because 
The relation is a function because for every 
The relation is a function because 
The relation is not a function because 
The relation is not a function because
The relation is not a function because 
Example Question #1 : Determine If A Relation Is A Function
Consider a family consisting of a two parents, Juan and Oksana, and their daughters Adriana and Laksmi. A relation 
The relation is not a function because (Laksmi,Juan) and (Laksmi,Oksana) both hold.
Even if the two parents had only one daughter, the relation would not be a function.
(Laksmi,Adriana) does not hold because Adriana is not Laksmi's child.
If the two parents had only one daughter, the relation would be a function.
(Adriana,Laksmi) does not hold because Laksmi is not Adriana's child and is a boy.
Even if the two parents had only one daughter, the relation would not be a function.
The statement
"Even if the two parents had only one daughter, the relation would not be a function."
is not true because if they had only one daughter, say Adriana, then the only relations that would exist would be (Juan, Adriana) and (Oksana,Adriana), which defines a function.
Example Question #3 : Determine If A Relation Is A Function
Which of the following relations is not a function?
The definition of a function requires that for each input (i.e. each value of 
Example Question #1 : Determine If A Relation Is A Function
Given the set of ordered pairs, determine if the relation is a function
Cannot be determined
Yes
No
No
A relation is a function if no single x-value corresponds to more than one y-value.
Because the mapping from 
the relation is NOT a function.
Example Question #1 : Determine If A Relation Is A Function
What equation is perpendicular to 
First find the reciprocal of the slope of the given function.
The perpendicular function is:
Now we must find the constant, 
solve for 
Example Question #5 : Determine If A Relation Is A Function
Is the following relation of ordered pairs a function?
Yes
No
Cannot be determined
Yes
A set of ordered pairs is a function if it passes the vertical line test.
Because there are no more than one corresponding 
Example Question #1 : Real Numbers
Which of the following is not true about a field. (Note: the real numbers 
For every element 
We have 
A field can be defined in many ways.
For every element 
There is an element 
For every element
It is not the case that for any element 
Example Question #1 : Modeling
John lives in Atlanta, but commutes every Monday to LaGrange where he has an apartment he stays in Monday-Friday for work. Each Monday he drives 350 miles to LaGrange. Once he arrives to his home away from home he is in walking distance of work and does not use his car for anything else. After 23 weeks his odometer shows 186,000 miles. Write an equation that models his odometer reading as a function of the number of weeks he has been driving after commencing his new job.
The rate of change of his mileage is 700 per week (350 x 2=700 there and back). The rate of change is the same thing as slope. Since we are looking for equation an equation that models his odometer reading as a function of the number of weeks he has been driving we can extract the point (23 , 18600) since after 23 weeks his odometer read 18,600 miles. Now we will use the point slope formula:
distribute the right side
isolate y
Example Question #1 : Linear Modeling
John lives in Atlanta, but commutes every Monday to LaGrange where he has an apartment he stays in Monday-Friday. Each Monday he drives 350 miles to LaGrange. Once he arrives to his apartment he is in walking distance of work and does not use his car for anything else. After 23 weeks his odometer shows 186,000 miles. Write an equation that models his odometer reading as a function of the number of weeks he has been driving after commencing his new job. Using the equation you just made, what is the y intercept or his original mileage before starting?
y intercept=153,800 miles
Need more information to solve.
y intercept=169,900 miles
y intercept=186,000 miles
y intercept=16,100 miles
y intercept=169,900 miles
The y intercept can be found by plugging in 0 for x in your original equation: y=700x+169,900 because at x=0 you can only reach the y axis and thus will find the y intercept.
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