Constructing a function's graph
Constructing a function graph is a Grade 7 math skill from Yoshiwara Intermediate Algebra where students build the graph of a function step by step: generating a table of values, plotting points in the coordinate plane, and connecting them to show the function shape.
Key Concepts
Property We can construct a graph for a function described by an equation by plotting points whose coordinates satisfy the equation. We choose several convenient values for $x$ and evaluate the function to find the corresponding $f(x)$ values.
Examples To graph $f(x) = x^2 + 1$, we can choose $x=2$. We find $f(2) = 2^2 + 1 = 5$, so we plot the point $(2, 5)$. For the same function, $f(x) = x^2 + 1$, we find $f(0) = 0^2 + 1 = 1$. This gives us the y intercept at $(0, 1)$. After calculating points like $( 2, 5)$, $(0, 1)$, and $(2, 5)$, connecting them reveals the U shape of the parabola.
Explanation To draw a function, create a table of values. Pick several inputs ($x$), calculate their outputs ($f(x)$) using the function's rule, and plot each $(x, f(x))$ coordinate pair. Then, connect the dots with a smooth curve.
Common Questions
How do you construct a function graph?
Choose several x-values, compute f(x) for each, create an (x, f(x)) table, plot each point, and connect them smoothly.
How many points do you need to construct a graph?
At minimum, 5 to 7 well-spaced points help you see the general shape. For linear functions, 3 points are sufficient.
Why should you include negative and positive x-values?
Including x-values from both sides of the y-axis shows the full behavior of the function, including symmetry.
How do you decide which x-values to use?
Choose x-values that include key features: zeros, the vertex, and enough surrounding points to show the curve shape.