1. In your own words, write the steps of performing a graphical transformation. Include any key reminders you think a students will forget in your description.
2. The graph of a function f(x) is illustrated. Use the graph of f(x) to perform the following graphical transformations. You do not need to show the shifted graph, you just need to list the 6 corresponding points. Answer each part seperately.
external image image002.jpg
(a) H(x) = f(x + 1) -2 (left 1 and down 2 units)
(b) Q(x) = 2f(x) (stretched by 2)
(c) P(x) = -f(x) (reflection over x-axis)
3. Suppose that the x-intercepts of the graph of f(x) are -5 and 3. Explain your thinking process or what helped you arrive at your answers.
(a) What are x-intercepts if y = f(x+2)? (shifted to the left two units)
(b) What are x-intercepts if y = f(x-2)? (shifted to the right two units)
(c) What are x-intercepts if y = 4f(x)? (stretched vertically by 4)
(d) What are x-intercepts if y = f(-x)? (reflected over the y-axis)
4. Suppose that the function f(x) is increasing on the interval (-1, 5). Explain your thinking process or what helped you arrive at your answers.
(a) Over which interval is the graph of y = f(x+2) increasing? (left 2 units)
(b) Over which interval is the graph of y = f(x-5) increasing? (right 5 units)
(c) Over which interval is the graph of y = f(x)-1 increasing? (down 1 unit)
(d) Over which interval is the graph of y = -f(x) increasing? (reflected over x-axis)
(e) Over which interval is the graph of y = f(-x) increasing? (reflected over y-axis)
2. The graph of a function f(x) is illustrated. Use the graph of f(x) to perform the following graphical transformations. You do not need to show the shifted graph, you just need to list the 6 corresponding points. Answer each part seperately.
(a) H(x) = f(x + 1) -2 (left 1 and down 2 units)
(b) Q(x) = 2f(x) (stretched by 2)
(c) P(x) = -f(x) (reflection over x-axis)
3. Suppose that the x-intercepts of the graph of f(x) are -5 and 3. Explain your thinking process or what helped you arrive at your answers.
(a) What are x-intercepts if y = f(x+2)? (shifted to the left two units)
(b) What are x-intercepts if y = f(x-2)? (shifted to the right two units)
(c) What are x-intercepts if y = 4f(x)? (stretched vertically by 4)
(d) What are x-intercepts if y = f(-x)? (reflected over the y-axis)
4. Suppose that the function f(x) is increasing on the interval (-1, 5). Explain your thinking process or what helped you arrive at your answers.
(a) Over which interval is the graph of y = f(x+2) increasing? (left 2 units)
(b) Over which interval is the graph of y = f(x-5) increasing? (right 5 units)
(c) Over which interval is the graph of y = f(x)-1 increasing? (down 1 unit)
(d) Over which interval is the graph of y = -f(x) increasing? (reflected over x-axis)
(e) Over which interval is the graph of y = f(-x) increasing? (reflected over y-axis)