SOLUTION: Suppose that the graph of a function f is known.Explain how the graph of y = f(x) + 2 differs from the graph of y = f(x + 2).

Algebra ->  Graphs -> SOLUTION: Suppose that the graph of a function f is known.Explain how the graph of y = f(x) + 2 differs from the graph of y = f(x + 2).       Log On


   

Question 1208124: Suppose that the graph of a function f is known.Explain how the graph of
y = f(x) + 2 differs from the graph of y = f(x + 2).
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52816) About Me  (Show Source):
You can put this solution on YOUR website!
.
Suppose that the graph of a function f is known. Explain how the graph of
y = f(x) + 2 differs from the graph of y = f(x + 2).
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    Graph y = f(x)+2 is obtained from the parent function graph by translating it 2 units vertically up.

    Graph y = f(x+2)  is obtained from the parent function graph by translating it along x-axis horizontally 2 units left.



Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Let's look at an example
f(x) = x^2
g(x) = f(x)+2 = x^2+2
h(x) = f(x+2) = (x+2)^2

Graph
graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Cx%5E2%2Cx%5E2%2B2%2C%28x%2B2%29%5E2%29
f(x) in red, g(x) in green, h(x) in blue.

g(x) is the result of shifting f(x) 2 units upward.
h(x) is the result of shifting f(x) 2 units to the left.

Two graphing tools I recommend are Desmos and GeoGebra. There are many other similar tools.