Let f(x) = e^(x – 2) + 3.
Describe in words how the graph of f can be obtained from the graph of y = e^x.
starting with the graph of y=e^x.
move it up three units.
move it to the right two units.
What does this mean exactly? How can I put this in to a sentence to answer the question? Thank you!
Describe in words how the graph of f can be obtained from the graph of y = e^x.
To obtain the graph of f(x) = e^(x - 2) + 3 from the graph of y = e^x, we can follow these steps:
1. Shift the graph horizontally: Since the variable x in f(x) is replaced with (x - 2), it means the graph of f is shifted 2 units to the right compared to y = e^x. This horizontal shift moves the entire graph to the right.
2. Shift the graph vertically: The "+3" term in f(x) means the graph of f is shifted 3 units upward compared to the graph of y = e^x. This vertical shift raises the entire graph.
By applying these shifts to the original graph of y = e^x, we get the graph of f(x) = e^(x - 2) + 3. The resulting graph will have the same shape as y = e^x but will be shifted 2 units to the right and 3 units upward.