Question 1

Which of the following represents the graph of $$y = f(x) + 3 if$$ $$y = f(x) is $$the original function?

Accepted Answer

The graph of $$y = f(x)$$ shifted 3 units upward.

Question 2

Given the function $$y = (x - 4)^2$, how is the graph of y$$ = $$x^2$$ transformed?

Accepted Answer

Shifted 4 units to the right.

Question 3

If $$y = \sqrt{x} + 5$$, what transformation has been applied to the parent function $$y = \sqrt{x}$$?

Accepted Answer

Shifted 5 units upward.

Question 4

Which equation represents the graph of $$y = x^2$ shifted 2 units downward and 3 units to the left?

Accepted Answer

$$y = (x + 3)^2$ - 2$$

Question 5

A medical researcher models the growth of bacteria with $$y = f(x)$$, where $$x is $$time in hours. If the initial measurement was taken 2 hours late, which function best represents the actual growth?

Accepted Answer

$$y = f(x + 2)$$

Question 6

Which transformation occurs when the function $$y = |x| is $$changed to $$y = |x - 3| + 4$$?

Accepted Answer

Shifted 3 units right and 4 units up.

Question 7

A quadratic function $$y = (x + 2)^2$ - 5$$ models the height of a projectile. What does the $$+2$$ inside the parentheses represent?

Accepted Answer

A shift 2 units to the left.

Question 8

If $$y = f(x - c)$$, what is the effect of increasing $$c on $$the graph of $$y = f(x)$$?

Accepted Answer

The graph shifts $$c$$ units to the right.

Question 9

Which of the following is the correct transformation for $$y = \sqrt{x}$$ shifted 4 units to the left and 3 units down?

Accepted Answer

$$y = \sqrt{x + 4} - 3$$

Question 10

A company tracks profit with $$y = f(x)$$, where $$x is $$months since launch. If the profit graph is shifted 6 units upward, which equation models this?

Accepted Answer

$$y = f(x) + 6$$

Question 11

Given $$y = |x - 2| + 5$$, what is the sequence of transformations applied to $$y = |x|$$?

Accepted Answer

Shift right 2, then up 5.

Question 12

If $$y = f(x) - d$$, what does the $$-d do to $$the graph of $$y = f(x)$$?

Accepted Answer

Shifts the graph $$d$$ units downward.

Question 13

A city’s population growth is modeled by $$y = f(x - 10) + 2000. $$What do the transformations represent?

Accepted Answer

Shift right 10 years, then up 2000 people.

Question 14

Which function represents the graph of $$y = x^2$ shifted left by 5 and up by 7?

Accepted Answer

$$y = (x + 5)^2$ + 7$$

Question 15

A scientist models temperature change with $$y = f(x + 3) - 8. $$What does this transformation do to the graph of $$y = f(x)$$?

Accepted Answer

Shifts left 3 units and down 8 units.

Question 16

If $$y = (x + 1)^2$ + 2$$, what is the order of transformations applied to $$y = x^2$?

Accepted Answer

Shift left 1, then up 2.

Question 17

Which of the following is the correct transformation for $$y = \sqrt{x - 6} + 4$$?

Accepted Answer

Shift right 6, then up 4.

Question 18

A function $$y = f(x) is $$shifted left by $$a$$ units and up by $$b$$ units. Which equation represents this transformation?

Accepted Answer

$$y = f(x + a) + b$$

Question 19

If $$y = |x - 1| + 2$$, which transformation is applied to $$y = |x|$$ first according to the general rule of thumb?

Accepted Answer

Horizontal shift right by 1.

Function Transformations: Vertical and Horizontal Shifts

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