Drawing Graphs from Tables Flashcards

All 5 cards in this deck

What are the steps to draw a graph from a table of values?

e.g. $y = 5 - x^3$ for $-2 \le x \le 2$

1. Substitute each $x$ into the equation: $x = -2$ gives $y = 13$
2. Plot the points: $(-2,13), (-1,6), (0,5), (1,4), (2,-3)$
3. Join them with a single smooth curve.

How should plotted points of a quadratic or cubic graph be joined?

With a smooth curve (freehand is fine) — not with ruled straight line segments.

True or false? When $x = -2$, the value of $x^2$ is $-4$.

False.
$(-2)^2 = 4$; squaring a negative number gives a positive result.

What symmetry should you see in a completed table of values for a quadratic?

The $y$-values repeat symmetrically either side of the turning point.
e.g. $\ldots, -3, -4, -3, \ldots$

Why can a table of values for $y = \frac{a}{x}$ never include $x = 0$?

Because dividing by $0$ is undefined, so the graph has no point there (the $y$-axis is an asymptote).