Given the parent function f(x) = 2^x, which graph shows f(x)+1?
1 answer:
Step-by-step explanation:
f(x) + n - move the graph n units up
f(x) - n - move the graph n units down
f(x + n) - move the graph n units to the left
f(x - n) - move the graph n units to the right
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We have f(x) = 2ˣ.
g(x) = f(x) + 1 - move the graph of f(x) one unit up.
<em>(look at the picture)</em>
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Explanation: To graph the equation y = x - 2, the idea is simple.
We pick three values for <em>x</em>, plug them into the
equation, and find the corresponding values for <em>y</em>.
In order to do this in an organized way, we set up a chart.
Down the left side we make a column for our x's, down the right side we make a column for our y's, and in the middle we make a column for the side of the equation that contains the <em>x</em>, in this case, x - 2.
So reading the chart from left to right, we have our <em>x</em> or what we plug into the equation, then we have the x - 2 or what happens to the x when we plug it into the equation, and finally we have our <em>y</em> or what we end up with after plugging <em>x</em> into the equation.
So our first step in filling out the chart is choosing
the x's that we want to plug into the equation.
When graphing lines, I always choose three x's,
a positive number, zero, and a negative number.
The easiest numbers to pick are usually 1, 0, and -1.
So for 1, we plug a 1 into the equation for <em>x</em>
and we have y = (1) - 2 or -1
For 0 we plug a 0 into the equation for <em>x</em>
and we have y = (0) - 2 or -2.
For -1 we plug a -1 into the equation for <em>x</em>
and we have y = (-1) - 2 or -3.
So our points are (1, -1), (0, -2), and (-1, -3).
I looked at the x and y column to find those points.
Since our domain is all real numbers, we can connect these points based on the pattern that they are forming on the graph which is a line.
I hope you don't find the solution too messy. If there is anything you don't get. Let me know and I will explain it:
