Math  /  Algebra

QuestionWhich transformations are applied to g(x)g(x) to produce the function f(x)f(x)? Complete the table below to show which transformation is used in the function.
f(x)=g(x)f(x) = -g(x) f(x)=g(x)7f(x) = g(x) - 7 f(x)=0.5g(x)f(x) = 0.5g(x) Translation down Reflection Compression

Studdy Solution

STEP 1

What is this asking? Given a function g(x)g(x), how do we transform it to get other functions? Watch out! Don't mix up translations, reflections, and compressions!
Each one does something totally different to our function.

STEP 2

1. Analyze f(x)=g(x)f(x) = -g(x)
2. Analyze f(x)=g(x)7f(x) = g(x) - 7
3. Analyze f(x)=0.5g(x)f(x) = 0.5g(x)

STEP 3

Alright, let's **start** with f(x)=g(x)f(x) = -g(x).
We're multiplying g(x)g(x) by 1-1.

STEP 4

Multiplying by 1-1 **reflects** the graph across the x-axis.
It's like flipping it upside down!
So, we have a **reflection** here.

STEP 5

Now, let's **look** at f(x)=g(x)7f(x) = g(x) - 7.
We're subtracting 77 from g(x)g(x).

STEP 6

Subtracting a **constant** from the function shifts the entire graph **down** by that constant.
In this case, it's 77 units **down**.
That's a **translation down**!

STEP 7

Finally, we have f(x)=0.5g(x)f(x) = 0.5g(x).
We're multiplying g(x)g(x) by 0.50.5, which is the same as multiplying by 12\frac{1}{2}.

STEP 8

Multiplying by a **number** between 00 and 11 **compresses** the graph vertically.
It's like squishing it down!
So, this is a **compression**.

STEP 9

f(x)=g(x)f(x) = -g(x) involves a **reflection**. f(x)=g(x)7f(x) = g(x) - 7 involves a **translation down**. f(x)=0.5g(x)f(x) = 0.5g(x) involves a **compression**.

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