Graph of a function
Graph of a function is a Grade 7 math concept from Yoshiwara Intermediate Algebra representing all ordered pairs (x, f(x)) plotted in the coordinate plane. Students learn to sketch graphs from equations or tables, identify key features, and apply the vertical line test.
Key Concepts
Property The point $(a, b)$ lies on the graph of the function $f$ if and only if $f(a) = b$. Each point on the graph of the function $f$ has coordinates $(x, f(x))$ for some value of $x$.
Examples If $f(5) = 8$, the point $(5, 8)$ is on the graph of the function $f$. If the point $( 1, 4)$ is on the graph of a function $g$, it means that $g( 1) = 4$. The coordinates of any point on the graph of $h$ can be written in the form $(x, h(x))$ for some input $x$.
Explanation A function's graph is a picture of all its input output pairs. The horizontal position (x coordinate) is the input, and the vertical position (y coordinate) is the corresponding output. It's a visual map of the function's behavior.
Common Questions
What is the graph of a function?
The graph of f(x) is the set of all points (x, f(x)) in the coordinate plane, one for each valid input x in the domain.
How do you sketch a graph from a function rule?
Create a table of input-output pairs, plot the points, and connect them smoothly according to the function behavior.
What is the vertical line test?
A curve is a function if every vertical line crosses it at most once.
What key features should you identify on a function graph?
Key features include x-intercepts, y-intercept, local maxima and minima, intervals of increase, and end behavior.