Example
Graph [latex]f(x)=−x+1[/latex].
Answer: Start with a table of values. You can choose different values for x, but once again, it’s helpful to include 0, some positive values, and some negative values.
If you think of f(x) as y, each row forms an ordered pair that you can plot on a coordinate grid.
[latex]f(−2)=−(−2)+1=2+1=3\\f(−1)=−(−1)+1=1+1=2\\f(0)=−(0)+1=0+1=1\\f(1)=−(1)+1=−1+1=0\\f(2)=−(2)+1=−2+1=−1[/latex]
x |
f(x) |
[latex]−2[/latex] |
[latex]3[/latex] |
[latex]−1[/latex] |
[latex]2[/latex] |
[latex]0[/latex] |
[latex]1[/latex] |
[latex]1[/latex] |
[latex]0[/latex] |
[latex]2[/latex] |
[latex]−1[/latex] |
Plot the points.
Answer
Since the points lie on a line, use a straight edge to draw the line. Try to go through each point without moving the straight edge.
In the following video we show another example of how to graph a linear function on a set of coordinate axes.
https://youtu.be/sfzpdThXpA8
These graphs are representations of a linear function. Remember that a function is a correspondence between two variables, such as
Example
Match the following functions with their graph.
a) [latex] \displaystyle f(x)=3{{x}^{2}}[/latex]
b) [latex] \displaystyle f(x)=-3{{x}^{2}}[/latex]
c)[latex] \displaystyle f(x)=\frac{1}{2}{{x}^{2}}[/latex]
a)
b)
c)
Answer:
Function a) [latex] \displaystyle f(x)=3{{x}^{2}}[/latex] means that inputs are squared and then multiplied by three, so the outputs will be greater than they would have been for [latex]f(x)=x^2[/latex]. This results in a parabola that has been squeezed, so the graph b) is the best match for this function.
Function b) [latex] \displaystyle f(x)=-3{{x}^{2}}[/latex] means that inputs are squared and then multiplied by negative three, so the outputs will be greater than they would have been for [latex]f(x)=x^2[/latex] so graph a) is the best match for this function.
Function c) [latex] \displaystyle f(x)=\frac{1}{2}{{x}^{2}}[/latex] means that inputs are squared then multiplied by [latex]\frac{1}{2}[/latex], so the outputs are less than they would be for [latex]f(x)=x^2[/latex]. This results in a parabola that has been opened wider than[latex]f(x)=x^2[/latex]. Graph c) is the best match for this function.
Answer
Function a) matches graph b)
Function b) matches graph a)
Function c) matches graph c)
If there is no
Example
Match the following functions with their graph.
a) [latex] \displaystyle f(x)={{x}^{2}}+3[/latex]
b) [latex] \displaystyle f(x)={{x}^{2}}-3[/latex]
a)
b)
Answer:
Function a) [latex] \displaystyle f(x)={{x}^{2}}+3[/latex] means square the inputs then add three, so every output will be moved up 3 units. the graph that matches this function best is b)
Function b) [latex] \displaystyle f(x)={{x}^{2}}-3[/latex] means square the inputs then subtract three, so every output will be moved down 3 units. the graph that matches this function best is a)