Reading a function's graph
Reading a function graph is a Grade 7 math skill from Yoshiwara Intermediate Algebra where students interpret the graphical representation of a function. This includes reading function values, identifying domain and range visually, and determining intercepts, maximums, and minimums from a graph.
Key Concepts
Property To find a function's value $f(x)$ from its graph, locate the input $x$ on the horizontal axis, move vertically to the graph, then move horizontally to find the output value on the vertical axis.
Examples To find $f(3)$, find $x=3$ on the horizontal axis. If the point on the graph above it is $(3, 2)$, then $f(3) = 2$. To find the value(s) of $x$ for which $f(x) = 5$, find $y=5$ on the vertical axis. If the graph has points at $( 1, 5)$ and $(4, 5)$, the solutions are $x= 1$ and $x=4$. The highest point on a graph shows the function's maximum value. If the highest point is $(2, 9)$, the maximum value is $9$.
Explanation Use the graph as a lookup tool. Start on the x axis for an input to find the output on the y axis. Or, start on the y axis for an output to find the input(s) on the x axis.
Common Questions
How do you read f(2) from a graph?
Find x = 2 on the horizontal axis, trace vertically to where the graph is, and read the y-value at that point. That y-value is f(2).
How do you find the domain from a graph?
The domain is the set of all x-values for which the graph exists. Look at the leftmost and rightmost points the graph covers.
How do you identify the range from a graph?
The range is the set of all y-values the graph reaches. Look at the lowest and highest points on the graph.
How do you find the x-intercepts from a graph?
The x-intercepts are where the graph crosses the x-axis (y = 0). Read the x-coordinates of those crossing points.