Lesson 3: Transforming Linear Functions — Practice Questions

1. 1. How does the graph of the equation $y = x + 5$ compare to the graph of the parent function $y = x$?

   • A. It is shifted 5 units up.
   • B. It is shifted 5 units down.
   • C. It is shifted 5 units to the right.
   • D. It is shifted 5 units to the left.

2. 2. The graph of the function $y = x + c$ is created by shifting the graph of $y = x$ down by 9 units. The value of $c$ must be ___.

3. 3. Which statement correctly describes the graph of $y = -x - 4$ compared to the graph of $y = -x$?

   • A. It is shifted 4 units down.
   • B. It is shifted 4 units up.
   • C. It is shifted 4 units to the right.
   • D. The slope is steeper.

4. 4. The graph of $y = x$ is shifted 11 units upward to create a new line. The equation of the new line is $y = x +$ ___.

5. 5. The graph of $y = x$ is translated so that it passes through the point $(0, 8)$. What is the equation of the new line?

   • A. $y = x + 8$
   • B. $y = x - 8$
   • C. $y = 8x$
   • D. $y = x$

6. 6. Given $f(x) = 3x - 2$ and its transformation $g(x) = f(x) + 5$. In a comparison table for these functions, what is the value of $g(x)$ when $x = 2$? The value is ___.

7. 7. In a comparison table for functions $f(x)$ and $g(x)$, the following values are observed: when $x=0$, $f(0)=4$ and $g(0)=2$. When $x=1$, $f(1)=7$ and $g(1)=5$. Which equation describes this relationship?

   • A. $g(x) = f(x) + 2$
   • B. $g(x) = f(x) - 2$
   • C. $g(x) = f(x-2)$
   • D. $g(x) = 2f(x)$

8. 8. Let $f(x) = 4x + 1$ and $g(x) = f(x-1)$. In a comparison table for these functions, what is the value of $g(x)$ when $x = 3$? The value is ___.

9. 9. A comparison table shows that for any input $x$, the value of $g(x)$ is the same as the value of $f(x)$ at an input of $x+2$. Which equation correctly represents this transformation?

   • A. $g(x) = f(x) + 2$
   • B. $g(x) = f(x) - 2$
   • C. $g(x) = f(x+2)$
   • D. $g(x) = f(x-2)$

10. 10. A comparison table is made for $f(x) = 5x - 3$ and its transformation $g(x) = f(x) + 4$. For the input $x=2$, the value of $f(2)$ is 7. What is the corresponding value of $g(2)$? The value is ___.