2.1 Basic functions (concepts)

1. Question

Which of the following relation(s) is/are not functions?

[math]4x-5y+6=0[/math]

[math](x-1)(y+2)=3[/math]

[math]y^2=x^2[/math]

[math]y=3\cdot x^{-3}[/math]

[math]x^2+2xy+y^2=1[/math]

2. Question

Which of the following function(s) is/are one-to-one?

[math]f(x)=\dfrac{2}{x-1}[/math]

[math]f(x)=\sqrt{(x-2)^2}[/math]

[math]f(x)=x+|x|[/math]

[math]f(x)=\dfrac{4x-7}{3}[/math]

[math]f(x)=\sqrt{4-x^2}[/math]

3. Question

If [math]f(x)=x^2+3[/math], which of the following is true?

The domain is [math]\mathbb{R}[/math]
The range is [math]\mathbb{R}[/math]

The domain is [math]\mathbb{R}[/math]
The range is [math]\{y|y\geq3\}[/math]

The domain is [math]\mathbb{R}[/math]
The range is [math]\{y|y\geq0\}[/math]

The domain is [math]\{x|x\geq-3\}[/math]
The range is [math]\{y|y\geq3\}[/math]

The domain is [math]\{x|x\geq3\}[/math]
The range is[math]\{y|y\geq3\}[/math]

4. Question

If [math]f(x)=-\sqrt{2x-1}[/math], which of the following is true?

The domain is [math]\{x|x\geq0.5\}[/math]
The range is [math]\{y|y\geq0\}[/math]

The domain is [math]\{x|x\geq0.5\}[/math]
The range is [math]\{y|y\leq0\}[/math]

The domain is [math]\{x|x\geq1\}[/math]
The range is [math]\{y|y\geq0\}[/math]

The domain is [math]\{x|x\geq1\}[/math]
The range is [math]\{y|y\leq0\}[/math]

5. Question

If [math]f(x)=1[/math], which of the following is true?

The domain is [math]\{1\}[/math]
The range is [math]\{1\}[/math]

The domain is [math]\{1\}[/math]
The range is [math]\mathbb{R}[/math]

The domain is [math]\mathbb{R}[/math]
The range is [math]\{1\}[/math]

The domain is [math]\mathbb{R}[/math]
The range is [math]\mathbb{R}[/math]

6. Question

If [math]f(x)=\dfrac{2021}{x+2021}[/math], which of the following is true?

The domain is [math]\{x|x\neq-2021\}[/math]
The range is [math]\{y|y\neq0\}[/math]

The domain is [math]\{x|x\neq-2021\}[/math]
The range is [math]\{y|y\neq2021\}[/math]

The domain is [math]\{x|x\neq-2021\}[/math]
The range is [math]\mathbb{R}[/math]

The domain is [math]\{x|x\neq2021\}[/math]
The range is [math]\{y|y\neq0\}[/math]

The domain is [math]\{x|x\neq2021\}[/math]
The range is [math]\{y|y\neq1\}[/math]

7. Question

If [math]f(x)=\sqrt{x+2}[/math] and [math]g(x)=\dfrac{1}{x}[/math], which of the following functions domains differes from the others?

[math]f(x)+g(x)[/math]

[math]f(x)g(x)[/math]

[math]\dfrac{g(x)}{f(x)}[/math]

These three functions have the same domain.

8. Question

If [math]f(x)=\dfrac{3}{\sqrt{1-x}}[/math], which of the following statements is true?

Domain: [math][1,\infty)[/math]
Range: [math][0,\infty)[/math]

Domain: [math](1,\infty)[/math]
Range: [math][0,\infty)[/math]

Domain: [math](-\infty,1][/math]
Range: [math](0,\infty)[/math]

Domain: [math](-\infty,1)[/math]
Range: [math](0,\infty)[/math]

9. Question

If [math]f(x)=-2|x-1|+5[/math], what is the range of [math]f(x)[/math]?

[math]\{y|y\leq5\}[/math]

[math]\{y|y<5\}[/math]

[math]\{y|y\geq5\}[/math]

[math]\{y|y>5\}[/math]

10. Question

If [math]f(x)=-(x-1)^2-7[/math], which of the following statements is true?

Domain: [math]\{x|x\neq1\}[/math]
Range: [math]\{y|y\leq-7\}[/math]

Domain: [math]\{x|x\geq1\}[/math]
Range: [math]\{y|y<-7\}[/math]

Domain: [math]\mathbb{R}[/math]
Range: [math]\{y|y<-7\}[/math]

Domain: [math]\mathbb{R}[/math]
Range: [math]\{y|y\leq-7\}[/math]

11. Question

If [math]f(x)=f(x)=3(3|3x|)^3+3[/math], what is the range of [math]f(x)[/math]?

[math]\{y|y\geq3\}[/math]

[math]\{y|y>3\}[/math]

[math]\{y|y\geq0\}[/math]

[math]\mathbb{R}[/math]

12. Question

What is the range of the equation [math]y=-|x-8|+3[/math]?

[math]\{y|y<3\}[/math]

[math]\{y|\leq3\}[/math]

[math]\{y|y<8\}[/math]

[math]\{y|y\leq8\}[/math]

13. Question

If [math]R[/math] is the range of [math]f(x)=\frac{x+2}{x^2-25}[/math], which of the following must be true?

[math]-5\notin R[/math]

[math]-2\notin R[/math]

[math]0\notin R[/math]

[math]5\notin R[/math]

14. Question

Which of the following satements is true about the relation [math]x+y^2=3[/math]?

This relation is a function, but it is not one to one.

This relation is a function, and it is one to one.

This relation is a function, but is is not linear.

This relation is not a function.

15. Question

Which relation is not a function?

[math]\{(0,1), (1,0), (2,0), (3,1)\}[/math]

[math]\{(-1,5), (-2,4), (-3,-3), (-4,4)\}[/math]

[math]\{(-1,1), (1,-1), (-1,3), (1,-3)\}[/math]

[math]\{(2,\displaystyle{\frac{1}{2}}), (4,\displaystyle{\frac{1}{4}}), (8,\displaystyle{\frac{1}{8}}), (16,\displaystyle{\frac{1}{16}})\}[/math]

16. Question

Which set represents the range of [math]\{(99,-2), (99,-3), (99,-4), (99,-5)\}[/math]?

[math]\{96, 99\}[/math]

[math]\{-2, -3, -4, -5\}[/math]

[math]\{x | x\in\mathbb{R}\}[/math]

[math]\{-2, -3, -4, -5, 96, 99\}[/math]

17. Question

Observe the figure. Which of the following statements is true?

The relation of the figure is a one to one function.

The relation of the figure is a many to one function.

The relation of the figure is not a function because it is one to many function.

The relation of the figure is not a function because it is many to many function.

18. Question

The relation below is a function. How many elements does its domain have?

19. Question

What is the domain of [math]g(t)=\sqrt{1-2t}[/math]?

[math](-\infty,0.5][/math]

[math](-\infty,0.5)[/math]

[math](0.5,\infty)[/math]

[math][0.5,\infty)[/math]

20. Question

What is the range of [math]g(x)=\displaystyle{\frac{x-3}{2x-3}}[/math]?

[math]\{y|y\neq0\}[/math]

[math]\{y|y\neq0.5\}[/math]

[math]\{y|y\neq1\}[/math]

[math]\{y|y\neq1.5\}[/math]

21. Question

If [math]f(x)=\dfrac{3x-1}{3x-5}[/math], then

(a) [math]f(\dfrac{2}{3})[/math]

(b) [math]f(-3)[/math]

(a)

(b)

22. Question

If [math]f(x)=|3-x^2|[/math], then

(a) [math]f(0)[/math]

(b) [math]f(-3)[/math]

(a)

(b)

23. Question

Use the graph of the function [math]f(x)[/math] shown to answer this question.

(a) Find [math]f(-4)[/math].

(b) Find [math]f\left(\displaystyle{\frac{1}{2}}\right)[/math].

(c) [math]f\left(\displaystyle{\frac{3}{2}}\right)[/math] is (positive or negative)

(d) For what negative numbers [math]x[/math] is [math]f(x)=-1[/math]?

(e) What is the maximum [math]x[/math]-intercept?

(f) What is the [math]y[/math]-intercept?

(a)

(b)

(c)

(d)

(e)

(f)

24. Question

If [math]y=\sqrt{x-2}[/math], which of the following value DO NOT meet the domain?

[math]2[/math]

[math]4[/math]

[math]\pi[/math]

[math]1[/math]

[math]3[/math]

25. Question

If [math]f(x)=3xg(x)[/math] and [math]f(3)=6[/math], then [math]g(3)[/math]

[math]\dfrac{6}{9}[/math]

[math]\dfrac{5}{9}[/math]

[math]\dfrac{7}{9}[/math]

[math]\dfrac{5}{8}[/math]

[math]\dfrac{5}{7}[/math]

26. Question

The graphs of the functions [math]f[/math] and [math]g[/math] are shown above. Which of the following true?

[math]g(x)=|f(-x)|[/math]

[math]g(x)=|f(x)|[/math]

[math]g(x)=f(-x)[/math]

[math]g(x)=-f(-x)[/math]

[math]g(x)=-f(x)[/math]

27. Question

In which of the following is [math]y[/math] a function of [math]x[/math]?
I.

[math]x[/math]	[math]y[/math]
[math]-2[/math]	[math]-10[/math]
[math]0[/math]	[math]-1[/math]
[math]1[/math]	[math]0[/math]
[math]-1[/math]	[math]1[/math]
[math]0[/math]	[math]2[/math]

II.

[math]x[/math]	[math]y[/math]
[math]-10[/math]	[math]-2[/math]
[math]-1[/math]	[math]0[/math]
[math]0[/math]	[math]1[/math]
[math]1[/math]	[math]-1[/math]
[math]2[/math]	[math]0[/math]

III.

[math]x[/math]	[math]y[/math]
[math]-2[/math]	[math]\frac{1}{2}[/math]
[math]-1[/math]	[math]\frac{1}{2}[/math]
[math]0[/math]	[math]\frac{1}{2}[/math]
[math]1[/math]	[math]\frac{1}{2}[/math]
[math]2[/math]	[math]\frac{1}{2}[/math]

I only

II only

I and II only

II and III only

I, and II, and III

28. Question

If the function [math]f[/math] is symmetric with respect to the line [math]x=3[/math] and if [math]f(-1)=-1[/math], what is the value of [math]f(7)[/math]?

[math]-7[/math]

[math]-1[/math]