Question 1

Which of the following functions is represented by the graph in the first image (a straight line passing through the origin with a slope of 1)?

Accepted Answer

$$f(x) = x$$

Question 2

The second image shows a graph opening upwards and passing through the origin. Which function does this graph represent?

Accepted Answer

$$f(x) = x^2$

Question 3

Which transformation is applied to $$f(x) = x^2$ to obtain f(x$$) = $$x^2 + 4$?

Accepted Answer

Vertical shift upward by 4 units

Question 4

If the graph of $$f(x) = x^3$ is transformed to f(x$$) = $$2x^3$$, what happens to the graph?

Accepted Answer

It is stretched vertically by a factor of 2

Question 5

Which of the following describes the transformation from $$f(x) = |x| to$$ $$f(x) = |x - 3|$$?

Accepted Answer

Horizontal shift right by 3 units

Question 6

The graph of $$f(x) = -x^2$ is obtained from f(x$$) = $$x^2 by $$which transformation?

Accepted Answer

Reflection in the x-axis

Question 7

Which function is piecewise-defined and has different rules for positive and negative values of $$x$$?

Accepted Answer

$$f(x) = |x|$$

Question 8

If $$f(x) = x^2$, what is the effect of the transformation f(x$$) = $$x^2 - 5$?

Accepted Answer

Vertical shift downward by 5 units

Question 9

Which transformation results in the graph of $$f(x) = -|x|$$ from $$f(x) = |x|$$?

Accepted Answer

Reflection in the x-axis

Question 10

A business models its profit with the function $$P(x) = |x - 2|. $$What is the minimum profit, and at what value of $$x$$ does it occur?

Accepted Answer

Minimum profit is 0 at $$x = 2$$

Question 11

Which of the following is the correct domain and range for the cube root function $$f(x) = \sqrt[3]{x}$$?

Accepted Answer

Domain: $$\mathbb{R}$$, Range: $$\mathbb{R}$$

Question 12

If $$f(x) = x^2$, what is the effect of the transformation f(x$$) = $$0.5x^2$$?

Accepted Answer

Vertical shrink by a factor of 0.5

Question 13

Which transformation is applied to $$f(x) = x to $$obtain $$f(x) = -x$$?

Accepted Answer

Reflection in the x-axis

Question 14

A company models its cost with $$C(x) = |x - 5| + 3. $$What is the minimum cost, and at what value of $$x$$ does it occur?

Accepted Answer

Minimum cost is 3 at $$x = 5$$

Question 15

Which of the following is a piecewise-defined function?

Accepted Answer

$$f(x) = |x|$$

Question 16

If $$f(x) = x^2$, what is the effect of the transformation f(x$$) = $$x^2 + 2$?

Accepted Answer

Vertical shift upward by 2 units

Question 17

Which transformation results in the graph of $$f(x) = f(-x)$$ from $$f(x)$$?

Accepted Answer

Reflection in the y-axis

Question 18

If $$f(x) = x^2$, what is the effect of the transformation f(x$$) = $$x^2 - 3$?

Accepted Answer

Vertical shift downward by 3 units

Question 19

Which of the following functions has domain $$x \geq 0$$ and range $$y \geq 0$$?

Accepted Answer

$$f(x) = \sqrt{x}$$

Functions and Graphs: Elementary Functions and Transformations 1.2

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