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 over the y axis by replacing x with -x.
Reflect a graph over the x axis by replacing y with -y.
Reflect a graph over 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.

y = (x + 2)² + 3

y = (x - 3)² + 3

y = (x + 2)² - 3

y = (x - 3)² - 3




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

y = x³ - 9



y = x³ + 9

y = x + 9



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 = e^x, 5 units to the left, and then reflecting in the y-axis.

y = e^5-x

y = e^x-5

y = e^x+5

y = e^x + 5



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













Question 7: Find an equation of the graph which is obtained by reflecting the graph of y = e^3-x in the y-axis.

y = e^x-3

y = e^3-x

y = e^3+x

y = e^x





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