Using Tables to Graph Functions
Use input-output tables to graph functions in Grade 9 Algebra. Choose strategic x-values, compute f(x), plot ordered pairs, and connect them accurately.
Key Concepts
Property You can use a table of ordered pairs to graph an equation.
Examples To graph $y = x^2$, a table might include $( 2, 4)$, $( 1, 1)$, $(0, 0)$, $(1, 1)$, and $(2, 4)$. Plotting these points reveals a U shaped parabola. For the linear equation $y = 5x 4$, a table could have points $(0, 4)$, $(1, 1)$, and $(2, 6)$. Plotting these points creates a straight line. To see if a graph matches $f(x) = \frac{1}{3}x + 4$, you can check if points from its table, like $(0,4)$ and $(3,5)$, lie on the graphed line.
Explanation This is like playing connect the dots, but with math! First, you choose a few input values for 'x' and plug them into the equation to find their partner 'y' values. Organize these (x, y) pairs in a table. Then, plot each point on the graph and connect them to reveal the function's shape, whether it's a line or a curve.
Common Questions
How do you use an input-output table to graph a function?
Choose at least five x-values, substitute each into the function to compute f(x), and record the ordered pairs. Plot each pair on the coordinate plane, then connect the points with a smooth curve or straight line.
Which x-values should you choose when making a function table?
Choose values that include negatives, zero, and positives to show the full behavior of the function. For square-root functions, use perfect squares; for quadratics, include the vertex x-value and values on both sides.
How can you use a table to determine if a graph is linear or non-linear?
Calculate the differences between consecutive y-values. If the first differences are constant, the function is linear. If you need second differences to find a pattern, it is quadratic. Non-constant differences indicate a non-linear function.