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. 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 = x^{3} - 9 in the line y = x. y = x^{3} - 9 y = x^{3} + 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 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 = e^{3-x} in the y-axis. y = e^{x-3} y = e^{3-x} y = e^{3+x} y = e^{x} Press the Submit button to see the results.