QuestionFind the function with an axis of symmetry at $x = -3$ : $f(x)=|x-3|$ , $f(x)=|x|+3$ , $f(x)=|x+3|$ , $f(x)=|x|-3$ .

Studdy Solution

STEP 1

Assumptions1. The axis of symmetry for a function is the vertical line that passes through the vertex of the graph. . For an absolute value function of the form $f(x) = |x - h|$ , the axis of symmetry is $x = h$ .
3. For an absolute value function of the form $f(x) = |x + h|$ , the axis of symmetry is $x = -h$ .

STEP 2

We are looking for a function with an axis of symmetry of -. This means we are looking for a function where $h = -$ or $-h = -$ .

STEP 3

First, let's consider the function $f(x) = |x -3|$ . The axis of symmetry for this function is $x =3$ , which is not equal to -3. So, this function does not have an axis of symmetry of -3.

STEP 4

Next, let's consider the function $f(x) = |x| +3$ . The "+3" does not affect the axis of symmetry, which for the function $|x|$ is $x =0$ . So, this function also does not have an axis of symmetry of -3.

STEP 5

Now, let's consider the function $f(x) = |x +3|$ . The axis of symmetry for this function is $x = -3$ , which is exactly what we're looking for. So, this function does have an axis of symmetry of -3.

STEP 6

Finally, let's consider the function $f(x) = |x| -3$ . The "-3" does not affect the axis of symmetry, which for the function $|x|$ is $x =0$ . So, this function also does not have an axis of symmetry of -3.
The function with an axis of symmetry of -3 is $f(x) = |x +3|$ .

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QuestionFind the function with an axis of symmetry at $x = -3$ : $f(x)=|x-3|$ , $f(x)=|x|+3$ , $f(x)=|x+3|$ , $f(x)=|x|-3$ .

Studdy Solution

STEP 1

STEP 2

We are looking for a function with an axis of symmetry of -. This means we are looking for a function where $h = -$ or $-h = -$ .

STEP 3

First, let's consider the function $f(x) = |x -3|$ . The axis of symmetry for this function is $x =3$ , which is not equal to -3. So, this function does not have an axis of symmetry of -3.

STEP 4

Next, let's consider the function $f(x) = |x| +3$ . The "+3" does not affect the axis of symmetry, which for the function $|x|$ is $x =0$ . So, this function also does not have an axis of symmetry of -3.

STEP 5

Now, let's consider the function $f(x) = |x +3|$ . The axis of symmetry for this function is $x = -3$ , which is exactly what we're looking for. So, this function does have an axis of symmetry of -3.

STEP 6

Finally, let's consider the function $f(x) = |x| -3$ . The "-3" does not affect the axis of symmetry, which for the function $|x|$ is $x =0$ . So, this function also does not have an axis of symmetry of -3.
The function with an axis of symmetry of -3 is $f(x) = |x +3|$ .

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QuestionFind the function with an axis of symmetry at x=−3x = -3x=−3: f(x)=∣x−3∣f(x)=|x-3|f(x)=∣x−3∣, f(x)=∣x∣+3f(x)=|x|+3f(x)=∣x∣+3, f(x)=∣x+3∣f(x)=|x+3|f(x)=∣x+3∣, f(x)=∣x∣−3f(x)=|x|-3f(x)=∣x∣−3.

Studdy Solution

STEP 1

STEP 2

We are looking for a function with an axis of symmetry of -. This means we are looking for a function where h=−h = -h=− or −h=−-h = -−h=−.

STEP 3

First, let's consider the function f(x)=∣x−3∣f(x) = |x -3|f(x)=∣x−3∣. The axis of symmetry for this function is x=3x =3x=3, which is not equal to -3. So, this function does not have an axis of symmetry of -3.

STEP 4

Next, let's consider the function f(x)=∣x∣+3f(x) = |x| +3f(x)=∣x∣+3. The "+3" does not affect the axis of symmetry, which for the function ∣x∣|x|∣x∣ is x=0x =0x=0. So, this function also does not have an axis of symmetry of -3.

STEP 5

Now, let's consider the function f(x)=∣x+3∣f(x) = |x +3|f(x)=∣x+3∣. The axis of symmetry for this function is x=−3x = -3x=−3, which is exactly what we're looking for. So, this function does have an axis of symmetry of -3.

STEP 6

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QuestionFind the function with an axis of symmetry at $x = -3$ : $f(x)=|x-3|$ , $f(x)=|x|+3$ , $f(x)=|x+3|$ , $f(x)=|x|-3$ .

We are looking for a function with an axis of symmetry of -. This means we are looking for a function where $h = -$ or $-h = -$ .

First, let's consider the function $f(x) = |x -3|$ . The axis of symmetry for this function is $x =3$ , which is not equal to -3. So, this function does not have an axis of symmetry of -3.

Next, let's consider the function $f(x) = |x| +3$ . The "+3" does not affect the axis of symmetry, which for the function $|x|$ is $x =0$ . So, this function also does not have an axis of symmetry of -3.

Now, let's consider the function $f(x) = |x +3|$ . The axis of symmetry for this function is $x = -3$ , which is exactly what we're looking for. So, this function does have an axis of symmetry of -3.