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Make a table of values to find points of both f(x) and h(x). Recall the form of a reflection in the y-axis.
Graph:
Transformation: The graph of h is a reflection in the y-axis from the graph of f.
We are asked to graph f(x)=3x+4 and h(x)=f(- x). Also, we need to find the transformations from the graph of f to the graph of h.
To graph f(x), we will first make a table of values.
x | 3x+4 | f(x) |
---|---|---|
0 | 3( 0)+4 | 4 |
-1 | 3( -1)+4 | 1 |
-2 | 3( -2)+4 | -2 |
Now, we can plot these points and connect them with a straight line to have the graph of f(x).
Let's recall the definition of a reflection in the y-axis. Changing the sign of a function's input reflects the original function in the y-axis. Original Function & Reflected Function y=f(x) & y=f( -x) Because we have h=f( -x), we can state that h is a reflection in the y-axis of f. To graph h, let's make a table of values taking some inputs from f and change their signs.
x | - x | f(- x) | h(x) |
---|---|---|---|
0 | 0 | 3( 0)+4 | 4 |
1 | -1 | 3( -1)+4 | 1 |
2 | -2 | 3( -2)+4 | -2 |
Now, we can graph h and f in the same coordinate plane.