Functions and graphs

Every function question comes down to one idea: $f (a) = b$ means $(a, b)$ is on the graph. Whether you're given a table, formula or picture, read points.

Here

f (2) = 0

, so

x = 2

is a zero, and

f (0) = - 2

is the

y

-intercept.

Work through it

$f (x) = 2 x^{2} - 3$ . Find $f (- 2)$ .

Parentheses. $2 (- 2)^{2} - 3$

Square first. $8 - 3 = 5$

$f (x) = 3 x + k$ and $f (2) = 11$ . Find $f (4)$ .

Find $k$ . $6 + k = 11$ , $k = 5$

Now evaluate. $12 + 5 = 17$

A table shows $f (1) = 4$ , $f (2) = 7$ , $f (3) = 10$ . Find the rule.

Each step adds 3.slope 3

At $x = 0$ . $1$ , so $f (x) = 3 x + 1$

Watch out for this

Reading $f (2)$ as $f \times 2$ .

It's the value at 2, not a product.

The short version

f (a) = b

means the point

(a, b)

is on the graph. Zeros are where

y = 0

. Substitute with parentheses.

Your turn

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