08. Graphs of Functions
Dated: 30-10-2024
Imagine a function1
\[f(x) = y = x + 2; x\ne 2\]
One way to graph is to find the intercepts.
x intercept
\[0 = x + 2\]
\[-2 = x\]
y intercept
\[y = 0 + 2\]
\[y = 2\]
Then, we can combine both points and get our line.2
Its graph will be
Translations
- \(f(x) + c\) translates the
graph\(c\) units up. - \(f(x) - c\) translates the
graph\(c\) units down. - \(f(x + c)\) translates the
graph\(c\) units left. - \(f(x - c)\) translates the
graph\(c\) units right.
Scaling
If a function1 is multiplied by a constant \(c\) , such that \(c \cdot f(x)\) then \(c\) is the vertical scaling factor of \(f(x)\).
Vertical line Test
We can check if a graph is of a function1 by drawing a vertical line of the form \(x = a\).
If this line intersects the graph at only one point then it is graph of a function.1
References
Read more about notations and symbols.