Digital SAT Math Test 6 Question 3

The graph of

y = f (x + 3) - 5

is shown. Which equation defines function

f

$f (x) = - \frac{2}{3} x + 2$
$f (x) = - \frac{2}{3} x + 9$
$f (x) = - \frac{2}{3} x - 5$
$f (x) = - \frac{2}{3} x + 3$

Answer:

Explanation

The correct answer is Choice B.

Determine the linear equation of the given graph. Then, apply the function transformation rules to find $f (x)$ .

Choices A, C, and D are incorrect and may result from algebraic mistakes.

✨ Expert's Tip ✨

Given $y = f (x)$ , substituting $x - a$ and $y - b$ into the function would translate the graph of the new function, $y = f (x - a) + b$ , horizontally by $a$ units and vertically by $p$ .

3/11

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