Math / Algebra

Question[3x] What kind of transformation converts the graph of $f(x)=7 x-3$ into the graph of $g(x)=-7 x-3 ?$ (x) reflection across the $x$ -axis horizontal shrink horizontal stretch reflection across the $y$ -axis Submit Work it out

Studdy Solution

STEP 1

What is this asking? Which transformation changes $f(x) = 7x - 3$ into $g(x) = -7x - 3$ ? Watch out! Don't mix up reflections across the x-axis and y-axis!

STEP 2

1. Analyze the Change
2. Identify the Transformation

STEP 3

Alright, let's compare our two functions: $f(x) = 7x - 3$ and $g(x) = -7x - 3$ .
Notice that the only difference is the sign of the coefficient of $x$ .
In $f(x)$ , it's a positive $7$ , while in $g(x)$ , it's a negative $7$ .

STEP 4

Think about what happens when we change the sign of the $x$ term.
If we plug in $x = 1$ into $f(x)$ , we get $f(1) = 7 \cdot 1 - 3 = 4$ .
Now, let's plug in $x = -1$ into $f(x)$ : $f(-1) = 7 \cdot (-1) - 3 = -10$ .

STEP 5

Now, let's check $g(x)$ .
Plugging in $x = 1$ gives us $g(1) = -7 \cdot 1 - 3 = -10$ .
And plugging in $x = -1$ gives us $g(-1) = -7 \cdot (-1) - 3 = 4$ .
Whoa! Notice how the outputs switched places!

STEP 6

This switching of outputs when we change the sign of the input is a classic sign of a reflection across the y-axis!
Think about it: if we have a point $(x, y)$ on the graph of $f(x)$ , then the point $(-x, y)$ will be on the graph of $g(x)$ .
This means we're keeping the y-value the same, but flipping the sign of the x-value, which is exactly what a reflection across the y-axis does!

STEP 7

The transformation that converts the graph of $f(x)$ into the graph of $g(x)$ is a reflection across the y-axis.

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Question[3x] What kind of transformation converts the graph of $f(x)=7 x-3$ into the graph of $g(x)=-7 x-3 ?$ (x) reflection across the $x$ -axis horizontal shrink horizontal stretch reflection across the $y$ -axis Submit Work it out

Studdy Solution

STEP 1

What is this asking? Which transformation changes $f(x) = 7x - 3$ into $g(x) = -7x - 3$ ? Watch out! Don't mix up reflections across the x-axis and y-axis!

STEP 2

1. Analyze the Change
2. Identify the Transformation

STEP 3

Alright, let's compare our two functions: $f(x) = 7x - 3$ and $g(x) = -7x - 3$ .
Notice that the only difference is the sign of the coefficient of $x$ .
In $f(x)$ , it's a positive $7$ , while in $g(x)$ , it's a negative $7$ .

STEP 4

Think about what happens when we change the sign of the $x$ term.
If we plug in $x = 1$ into $f(x)$ , we get $f(1) = 7 \cdot 1 - 3 = 4$ .
Now, let's plug in $x = -1$ into $f(x)$ : $f(-1) = 7 \cdot (-1) - 3 = -10$ .

STEP 5

Now, let's check $g(x)$ .
Plugging in $x = 1$ gives us $g(1) = -7 \cdot 1 - 3 = -10$ .
And plugging in $x = -1$ gives us $g(-1) = -7 \cdot (-1) - 3 = 4$ .
Whoa! Notice how the outputs switched places!

STEP 6

STEP 7

The transformation that converts the graph of $f(x)$ into the graph of $g(x)$ is a reflection across the y-axis.

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Question[3x] What kind of transformation converts the graph of f(x)=7x−3f(x)=7 x-3f(x)=7x−3 into the graph of g(x)=−7x−3?g(x)=-7 x-3 ?g(x)=−7x−3? (x) reflection across the xxx-axis horizontal shrink horizontal stretch reflection across the yyy-axis Submit Work it out

Studdy Solution

STEP 1

What is this asking? Which transformation changes f(x)=7x−3f(x) = 7x - 3f(x)=7x−3 into g(x)=−7x−3g(x) = -7x - 3g(x)=−7x−3? Watch out! Don't mix up reflections across the x-axis and y-axis!

STEP 2

1. Analyze the Change2. Identify the Transformation

STEP 3

Alright, let's **compare** our two functions: f(x)=7x−3f(x) = 7x - 3f(x)=7x−3 and g(x)=−7x−3g(x) = -7x - 3g(x)=−7x−3.Notice that the only difference is the sign of the **coefficient** of xxx.In f(x)f(x)f(x), it's a **positive** 777, while in g(x)g(x)g(x), it's a **negative** 777.

STEP 4

STEP 5

STEP 6

STEP 7

The transformation that converts the graph of f(x)f(x)f(x) into the graph of g(x)g(x)g(x) is a reflection across the y-axis.

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Question[3x] What kind of transformation converts the graph of $f(x)=7 x-3$ into the graph of $g(x)=-7 x-3 ?$ (x) reflection across the $x$ -axis horizontal shrink horizontal stretch reflection across the $y$ -axis Submit Work it out

What is this asking? Which transformation changes $f(x) = 7x - 3$ into $g(x) = -7x - 3$ ? Watch out! Don't mix up reflections across the x-axis and y-axis!

1. Analyze the Change
2. Identify the Transformation

Alright, let's compare our two functions: $f(x) = 7x - 3$ and $g(x) = -7x - 3$ .
Notice that the only difference is the sign of the coefficient of $x$ .
In $f(x)$ , it's a positive $7$ , while in $g(x)$ , it's a negative $7$ .

The transformation that converts the graph of $f(x)$ into the graph of $g(x)$ is a reflection across the y-axis.