QuestionDetermine the $x$ value where the piecewise function $f(x)=\begin{cases}9 x^{2}-4 x+4 & \text{if } x<1 \\ -7 x^{2}-8 x+3 & \text{if } x \geq 1\end{cases}$ is discontinuous.

Studdy Solution

STEP 1

Assumptions1. The given function is a piecewise function defined as follows $f(x)=\left\{\begin{array}{ll}9 x^{}-4 x+4 & \text { if } x<1 \\ -7 x^{}-8 x+3 & \text { if } x \geq1\end{array}\right.$
. We are looking for the $x$ value at which this function is discontinuous.

STEP 2

A piecewise function is discontinuous at a point if the two pieces of the function do not meet at that point. In this case, we need to check if the two pieces of the function meet at $x=1$ .

STEP 3

First, we need to find the value of the function at $x=1$ for the first piece of the function. We do this by substituting $x=1$ into the equation for the first piece of the function.
$f(1)=9(1)^{2}-(1)+$

STEP 4

Calculate the value of the function at $x=1$ for the first piece of the function.
$f(1)=9(1)^{2}-4(1)+4=9-4+4=9$

STEP 5

Next, we need to find the value of the function at $x=1$ for the second piece of the function. We do this by substituting $x=1$ into the equation for the second piece of the function.
$f(1)=-7(1)^{2}-8(1)+3$

STEP 6

Calculate the value of the function at $x=1$ for the second piece of the function.
$f(1)=-(1)^{2}-8(1)+3=--8+3=-12$

STEP 7

Compare the values of the function at $x=1$ for the two pieces of the function. If the values are not equal, then the function is discontinuous at $x=1$ .
The function is discontinuous at $x=1$ because $f(1)=9$ for the first piece of the function and $f(1)=-12$ for the second piece of the function, and these values are not equal.
So, the $x$ value at which the function is discontinuous is $x=1$ .

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QuestionDetermine the $x$ value where the piecewise function $f(x)=\begin{cases}9 x^{2}-4 x+4 & \text{if } x<1 \\ -7 x^{2}-8 x+3 & \text{if } x \geq 1\end{cases}$ is discontinuous.

Studdy Solution

STEP 1

Assumptions1. The given function is a piecewise function defined as follows $f(x)=\left\{\begin{array}{ll}9 x^{}-4 x+4 & \text { if } x<1 \\ -7 x^{}-8 x+3 & \text { if } x \geq1\end{array}\right.$
. We are looking for the $x$ value at which this function is discontinuous.

STEP 2

A piecewise function is discontinuous at a point if the two pieces of the function do not meet at that point. In this case, we need to check if the two pieces of the function meet at $x=1$ .

STEP 3

First, we need to find the value of the function at $x=1$ for the first piece of the function. We do this by substituting $x=1$ into the equation for the first piece of the function.
$f(1)=9(1)^{2}-(1)+$

STEP 4

Calculate the value of the function at $x=1$ for the first piece of the function.
$f(1)=9(1)^{2}-4(1)+4=9-4+4=9$

STEP 5

Next, we need to find the value of the function at $x=1$ for the second piece of the function. We do this by substituting $x=1$ into the equation for the second piece of the function.
$f(1)=-7(1)^{2}-8(1)+3$

STEP 6

Calculate the value of the function at $x=1$ for the second piece of the function.
$f(1)=-(1)^{2}-8(1)+3=--8+3=-12$

STEP 7

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QuestionDetermine the xxx value where the piecewise function f(x)={9x2−4x+4if x<1−7x2−8x+3if x≥1f(x)=\begin{cases}9 x^{2}-4 x+4 & \text{if } x<1 \\ -7 x^{2}-8 x+3 & \text{if } x \geq 1\end{cases}f(x)={9x2−4x+4−7x2−8x+3​if x<1if x≥1​ is discontinuous.

Studdy Solution

STEP 1

STEP 2

A piecewise function is discontinuous at a point if the two pieces of the function do not meet at that point. In this case, we need to check if the two pieces of the function meet at x=1x=1x=1.

STEP 3

First, we need to find the value of the function at x=1x=1x=1 for the first piece of the function. We do this by substituting x=1x=1x=1 into the equation for the first piece of the function.f(1)=9(1)2−(1)+f(1)=9(1)^{2}-(1)+f(1)=9(1)2−(1)+

STEP 4

Calculate the value of the function at x=1x=1x=1 for the first piece of the function.f(1)=9(1)2−4(1)+4=9−4+4=9f(1)=9(1)^{2}-4(1)+4=9-4+4=9f(1)=9(1)2−4(1)+4=9−4+4=9

STEP 5

Next, we need to find the value of the function at x=1x=1x=1 for the second piece of the function. We do this by substituting x=1x=1x=1 into the equation for the second piece of the function.f(1)=−7(1)2−8(1)+3f(1)=-7(1)^{2}-8(1)+3f(1)=−7(1)2−8(1)+3

STEP 6

Calculate the value of the function at x=1x=1x=1 for the second piece of the function.f(1)=−(1)2−8(1)+3=−−8+3=−12f(1)=-(1)^{2}-8(1)+3=--8+3=-12f(1)=−(1)2−8(1)+3=−−8+3=−12

STEP 7

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QuestionDetermine the $x$ value where the piecewise function $f(x)=\begin{cases}9 x^{2}-4 x+4 & \text{if } x<1 \\ -7 x^{2}-8 x+3 & \text{if } x \geq 1\end{cases}$ is discontinuous.

A piecewise function is discontinuous at a point if the two pieces of the function do not meet at that point. In this case, we need to check if the two pieces of the function meet at $x=1$ .

First, we need to find the value of the function at $x=1$ for the first piece of the function. We do this by substituting $x=1$ into the equation for the first piece of the function.
$f(1)=9(1)^{2}-(1)+$

Calculate the value of the function at $x=1$ for the first piece of the function.
$f(1)=9(1)^{2}-4(1)+4=9-4+4=9$

Next, we need to find the value of the function at $x=1$ for the second piece of the function. We do this by substituting $x=1$ into the equation for the second piece of the function.
$f(1)=-7(1)^{2}-8(1)+3$

Calculate the value of the function at $x=1$ for the second piece of the function.
$f(1)=-(1)^{2}-8(1)+3=--8+3=-12$