how do you gfraph a function such as
g(x)= x +7 then compare it to the graph of f(x) =x?
this is very confusing...
make a table of values for each one,
graph it
you should get two parallel lines
ohh, you mean like an x and y table?
yes
so for the x side, is it better to start off with the number zero, or do you have any suggestions?
I usually use zero for my first x, but you can use any x you feel like.
remember you want to graph the points, so don't pick any silly numbers.
stick with 1's and 2's etc.
thanks a bunch! you really helped!
Graphing functions can sometimes seem confusing, but let's break it down step by step.
To graph the function g(x) = x + 7, we need to plot several points on a coordinate plane and connect them to form a line. Here's how you can do it:
1. Choose some values for x. Let's start with a few numbers to keep it simple. You can choose any values you want, but let's use -2, 0, and 2 for this example.
2. Substitute the chosen x-values into the function g(x) = x + 7 to find the corresponding y-values. Plug in -2, 0, and 2 one by one into the equation and solve for y:
For x = -2: g(-2) = -2 + 7 = 5
For x = 0: g(0) = 0 + 7 = 7
For x = 2: g(2) = 2 + 7 = 9
3. Plot the points on the coordinate plane. For each (x, y) pair, locate the x-value on the x-axis and the y-value on the y-axis, and mark the point on the graph.
Point A: (-2, 5)
Point B: (0, 7)
Point C: (2, 9)
4. Connect the points. Draw a straight line passing through all the plotted points. This line represents the graph of g(x) = x + 7.
Now, to compare it with the graph of f(x) = x, we can plot the function f(x) using a similar process. However, f(x) = x is a straight line passing through the origin (0, 0) with a slope of 1. So, its graph will be a straight line that intersects the y-axis at the origin.
By comparing the two graphs, you will notice that g(x) = x + 7 is a parallel line to f(x) = x, but it is shifted upward by 7 units. The graphs have the same slope, which means their steepness is the same, but they differ in their y-intercept (where the line intersects the y-axis).
I hope this explanation helps clear up any confusion. Graphing functions can take a little practice, so don't worry if it feels overwhelming at first.