Big Ideas Math Algebra 1, 2015
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Big Ideas Math Algebra 1, 2015 View details
Chapter Review
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Exercise 27 Page 167

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:

answer graph

Transformation: The graph of h is a reflection in the y-axis from the graph of f.

Practice makes perfect

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.

Graph of f(x)

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).

graph of f

Graph of h(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.

functions graph