To sketch the graph of the function [tex]\( f(x) = |5x - 5| \)[/tex], we first create a table of values for specific points.
We calculate [tex]\( f(x) \)[/tex] for the given values of [tex]\( x \)[/tex]:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) = |5x - 5| \\
\hline
-5 & 30 \\
\hline
-2 & 15 \\
\hline
0 & 5 \\
\hline
1 & 0 \\
\hline
2 & 5 \\
\hline
5 & 20 \\
\hline
\end{array}
\][/tex]
Now we can use these points to sketch the graph of [tex]\( f(x) = |5x - 5| \)[/tex]:
1. Point (-5, 30): Start at [tex]\( x = -5 \)[/tex], [tex]\( y = 30 \)[/tex].
2. Point (-2, 15): Next point at [tex]\( x = -2 \)[/tex], [tex]\( y = 15 \)[/tex].
3. Point (0, 5): Next point at [tex]\( x = 0 \)[/tex], [tex]\( y = 5 \)[/tex].
4. Point (1, 0): Next point at [tex]\( x = 1 \)[/tex], [tex]\( y = 0 \)[/tex]. This is where there is a corner in the absolute value function.
5. Point (2, 5): Next point at [tex]\( x = 2 \)[/tex], [tex]\( y = 5 \)[/tex].
6. Point (5, 20): Lastly, point at [tex]\( x = 5 \)[/tex], [tex]\( y = 20 \)[/tex].
Plot these points on the coordinate plane. The absolute value function [tex]\( f(x) = |5x - 5| \)[/tex] creates a V-shape graph, with its vertex at [tex]\( (1,0) \)[/tex].
After plotting, draw a line starting from the point [tex]\((-5, 30)\)[/tex] decreasing to the point [tex]\((1, 0)\)[/tex], and then increasing to the point [tex]\((5, 20)\)[/tex]. This forms the V-shaped graph characteristic of absolute value functions.
