# Translations and Reflections of Graphs

## Precalculus Quiz

Translations of graphs:
Translate a graph m (m > 0) units to the right, by replacing x with x - m.
Translate a graph m (m > 0) units to the left, by replacing x with x + m.
Translate a graph m (m > 0) units up, by replacing y with y - m.
Translate a graph m (m > 0) units down, by replacing y with y + m.

Reflections of graphs:
Reflect a graph in the y axis by replacing x with -x.
Reflect a graph in the x axis by replacing y with -y.
Reflect a graph in the x = y line by replacing x with y and y with x.

Question 1: Find an equation of the curve which results by translating the graph of y = (x - 1)2, 2 units to the right and 3 units down.

Question 2: Find an equation of the graph which is obtained by reflecting the graph of y = x3 - 9 in the line y = x.

Question 3: Find an equation of the curve which results by translating 6 units to the right and 4 units up the graph of:

Question 4: Find an equation of the curve which results by translating 2 units to the left and 3 units down the graph of:

Question 5: Find an equation of the graph which results from shifting the graph of y = ex, 5 units to the left, and then reflecting in the y-axis.

Question 6: Find an equation of the graph which is obtained by reflecting in the line y = x the graph of:

Question 7: Find an equation of the graph which is obtained by reflecting the graph of y = e3-x in the y-axis.

Press the Submit button to see the results.