Functions Translations and Reflections




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.








1. Given f(x) = x2 + x - 3, what is the equation of the function g(x), if the graph of g(x) is found by shifting the graph of f(x) 2 units up?
















2. Given f(x) = x2 + 5x, what is the equation of the function g(x), if the graph of g(x) is found by shifting the graph of f(x) 1 unit left?












3. Given f(x) = x3, what is the equation of the function g(x), if the graph of g(x) is found by shifting the graph of f(x) 2 units left and 3 units down?












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.













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