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# Maths Topic 5: Real Functions Trivia Quiz

### The quiz will test you on basic real functions, including concepts such as domain and range, odd and even functions and limits. You will need a pen, paper and a calculator for this quiz. Good luck.

A multiple-choice quiz by dialga483. Estimated time: 3 mins.

Author
Time
3 mins
Type
Multiple Choice
Quiz #
366,047
Updated
Dec 03 21
# Qns
15
Difficulty
Average
Avg Score
10 / 15
Plays
205
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Question 1 of 15
1. If f(x)=x^2+3x+1, then what is the value of f(-2)? Hint

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Question 2 of 15
2. If f(x)=x^5-x^2, then what is the value of f(3)? Hint

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Question 3 of 15
3. If a function is odd, then which statement is true? Hint

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Question 4 of 15
4. Which of the following functions is even? Hint

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Question 5 of 15
5. What is the domain of the function f(x)=1/sqrt(x-5)? Hint

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Question 6 of 15
6. What is the range of the function f(x)=1/(x-4)? Hint

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Question 7 of 15
7. What is the y-intercept of the linear function x+2y=3? Hint

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Question 8 of 15
8. What are the x-intercepts of the parabola y=x^2+2x-3? Hint

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Question 9 of 15
9. If a circle has equation (x-3)^2+(y-1)^2=4, then which co-ordinates represent the centre of the circle? Hint

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Question 10 of 15
10. What is the correct equation for a semi-circle that lies above the x-axis and has a y-intercept and radius of 3? Hint

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Question 11 of 15
11. What is the smallest possible y-value for the function y=abs(x)-1? Hint

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Question 12 of 15
12. For the exponential functions y=a^x and y=a^(-x), where a is any positive constant, the y-intercept is always equal to what? Hint

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Question 13 of 15
13. What is the limit of (x-2)/(x^2-4) as x approaches 2? Hint

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Question 14 of 15
14. What are the vertical and horizontal asymptotes of the hyperbola y=1/(x+2)? Hint

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Question 15 of 15
15. What is the domain of the function f(x)=log(x-3)? Hint

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Quiz Answer Key and Fun Facts
1. If f(x)=x^2+3x+1, then what is the value of f(-2)?

To solve this question, we need to substitute x=-2, for each x term in the function.
So,
If f(x)=x^2+3x+1
f(-2)=(-2)^2+3(-2)+1
f(-2)=4-6+1
f(-2)=-1
2. If f(x)=x^5-x^2, then what is the value of f(3)?

To solve this question, we need to substitute x=3, for each x term in the function
So,
If f(x)=x^5-x^2
f(3)=(3)^5-(3)^2
f(3)=243-9
f(3)=234
3. If a function is odd, then which statement is true?

To show that a function is odd, it must first be proved that it isn't even by using the rule f(x)=f(-x). Then using f(-x)=-f(x), it can be proven whether or not a function is odd.
4. Which of the following functions is even?

For a function to be even, it must first satisfy the rule f(x)=f(-x). Out of the possible answers, f(x)=x^2+3 is the only possible solution.
So,
f(x)=x^2+3
f(-x)=(-x)^2+3
f(-x)=x^2+3
f(-x)=f(x)
Therefore, f(x)=x^2+3 is the correct solution.
5. What is the domain of the function f(x)=1/sqrt(x-5)?

If x=5 was subbed into the equation, then the denominator would equal 0, giving an undefined result. If any number less than 5 was subbed in, then this would give a non-real result. Therefore, any number greater than 5 would give a real result, making the domain x greater than 5.
6. What is the range of the function f(x)=1/(x-4)?

Answer: all real y, y can't equal 0

The function f(x)=1/(x-4) resembles a hyperbola with a horizontal asymptote at y=0. Therefore, the range of f(x) is all real y, where y can't be equal 0.
7. What is the y-intercept of the linear function x+2y=3?

To find the y-intercept of a function, we simply need to sub in x=0.
So, subbing in x=0 gives,
2y=3
y=3/2
y=1.5
8. What are the x-intercepts of the parabola y=x^2+2x-3?

To find the x-intercepts, we simply sub in y=0.
This gives, x^2+2x-3=0, which we can solve as a quadratic equation.
So,
x^2+2x-3=0
(x+3)(x-1)=0
Therefore, x=-3, x=1
9. If a circle has equation (x-3)^2+(y-1)^2=4, then which co-ordinates represent the centre of the circle?

The general equation of a circle is (x-h)^2+(y-k)^2=r^2, where (h,k) is the centre of the circle and r is the radius. From the information in the question, we can work out that the centre of the circle is (3,1).
10. What is the correct equation for a semi-circle that lies above the x-axis and has a y-intercept and radius of 3?

The general equation for a semi-circle that lies above the x-axis is y=sqrt(r^2-x^2), where r is the radius of the semi-circle. The question tell us that the radius is 3, therefore, we can work out that the correct equation for the semi-circle is y=sqrt(9-x^2).
11. What is the smallest possible y-value for the function y=abs(x)-1?

To solve this question, we would first need to use the graph y=abs(x). From this, we can see that the smallest y-value lies at y=0. Using abs(x)-1, this pushes abs(x) down 1 unit, making the smallest y-value at y=-1.
12. For the exponential functions y=a^x and y=a^(-x), where a is any positive constant, the y-intercept is always equal to what?

To solve this question, we can simply sub in x=0. This gives us y=a^0. Now using index laws, any number to the power of 0 will give a result of 1.
Therefore, the y-intercept of y=a^x and y=a^(-x) will always be equal to 1.
13. What is the limit of (x-2)/(x^2-4) as x approaches 2?

To solve this question, we first need to simplify the given equation.
So,
(x-2)/(x^2-4)
=(x-2)/((x-2)(x+2))
=1/(x+2)
Now sub in x=2
=1/(2+2)
=1/4
Therefore, the limit is 1/4.
14. What are the vertical and horizontal asymptotes of the hyperbola y=1/(x+2)?

To solve this question, we need to find out what values x and y cannot be equal to.
For the vertical asymptote,
x+2=0
x=-2
Therefore, the vertical asymptote is at x=-2, since if we sub this in, we would get an undefined result.
For the horizontal asymptote, since the graph isn't translated up or down, and it asymptotes towards the x-axis, this makes the horizontal asymptote y=0.
15. What is the domain of the function f(x)=log(x-3)?