Question 1

Which of the following equations best represents the function shown in the first image (V-shaped graph with vertex at (5,0))?

Accepted Answer

$$f(x) = |x - 5|$$

Question 2

The second image shows a V-shaped graph with a vertex at (1,3). Which equation matches this graph?

Accepted Answer

$$f(x) = -|x - 1| + 3$$

Question 3

Which of the following best describes the transformation from $$f(x) = |x| to $$the function in the first image?

Accepted Answer

Shifted right 5 units

Question 4

In the third image (multiple parabolas), which function would produce the narrowest parabola?

Accepted Answer

$$f(x) = 3x^2$

Question 5

The graph in the fourth image (cubic-like, with two turning points) is most likely the graph of which type of function?

Accepted Answer

A cubic polynomial

Question 6

Which of the following statements is true about the function in the fifth image (polynomial with three turning points)?

Accepted Answer

The degree of the polynomial is at least 4

Question 7

In the sixth image (polynomial with a local maximum and minimum), what is the minimum possible degree of the polynomial?

Accepted Answer

3

Question 8

The seventh image shows a polynomial with two 'bounces' at the x-axis. What does this indicate about the zeros at those points?

Accepted Answer

They are zeros of even multiplicity

Question 9

In the eighth image (rational function with vertical asymptotes at $$x = -2$$ and $$x = 2$$), which of the following could be the equation for this function?

Accepted Answer

$$f(x) = \frac{1}{(x+2)(x-2)}$$

Question 10

The ninth image shows a rational function with vertical asymptotes at $$x = -3$$ and $$x = 3. $$Which of the following is the most likely equation for this function?

Accepted Answer

$$f(x) = \frac{1}{(x+3)(x-3)}$$

Question 11

In the tenth image, the rational function has a vertical asymptote at $$x = 2$$ and a horizontal asymptote at $$y = -2. $$Which equation could represent this function?

Accepted Answer

$$f(x) = \frac{x-1}{x-2} - 2$$

Question 12

The eleventh image shows a rational function with a vertical asymptote at $$x = -2$$ and a horizontal asymptote at $$y = -2. $$Which equation could represent this function?

Accepted Answer

$$f(x) = \frac{1}{x+2} - 2$$

Question 13

In the twelfth image, the rational function has vertical asymptotes at $$x = -3$$ and $$x = 3$$, and a horizontal asymptote at $$y = -2. $$Which equation could represent this function?

Accepted Answer

$$f(x) = \frac{1}{(x+3)(x-3)} - 2$$

Question 14

The thirteenth image shows a rational function with a vertical asymptote at $$x = 2$$ and a horizontal asymptote at $$y = 2. $$Which equation could represent this function?

Accepted Answer

$$f(x) = \frac{x+1}{x-2} + 2$$

Question 15

The fourteenth image shows a rational function with a vertical asymptote at $$x = -3$$ and a horizontal asymptote at $$y = 2. $$Which equation could represent this function?

Accepted Answer

$$f(x) = \frac{1}{x+3} + 2$$

Absolute Value, Power, Polynomial, and Rational Functions: Key Concepts and Graphical Analysis

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