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Let

f(x)=-x^{2}

/ 2. If the graph of

f(x)

is translated 2 units up and 3 un...

Sep 23, 2024

Generated Graph

Solution by Steps

step 2

To translate the graph 3 units left, we replace

x

with

(x + 3)

g(x) = -\frac{(x + 3)^2}{2} + 2

step 3

Now, we simplify

g(x)

g(x) = -\frac{(x^2 + 6x + 9)}{2} + 2 = -\frac{x^2}{2} - 3x - \frac{9}{2} + 2 = -\frac{x^2}{2} - 3x - \frac{5}{2}

step 4

To find

g(1/2)

, we substitute

x = 1/2

g(1/2) = -\frac{(1/2)^2}{2} - 3(1/2) - \frac{5}{2} = -\frac{1/8}{2} - \frac{3}{2} - \frac{5}{2} = -\frac{1}{16} - \frac{3}{2} - \frac{5}{2}

step 5

Simplifying further:

g(1/2) = -\frac{1}{16} - \frac{8}{16} - \frac{40}{16} = -\frac{49}{16}

. This does not match any of the answer choices, so we need to check our calculations

Key Concept

Graph Translation

Explanation

Translating a graph involves shifting it vertically and horizontally, which can be done by adjusting the function accordingly.