QuestionFind $k$ in the function $g(x)=-3\left[\frac{1}{2(x-3)}\right]+1$ given $a=-3$ , $d=3$ , $c=1$ .

Studdy Solution

STEP 1

Assumptions1. The function is given as $g(x)=-3\left[\frac{1}{(x-3)}\right]+1$ . The general form of the function is $f(x) = a[k(x-d)] + c$
3. The values of $a$ , $d$ , and $c$ are given as $a=-3$ , $d=3$ , and $c=1$
4. We need to find the value of $k$

STEP 2

We can write the given function in the form of $f(x) = a[k(x-d)] + c$ .
$g(x)=-\left[\frac{1}{2(x-)}\right]+1 = a[k(x-d)] + c$

STEP 3

Now, we can equate the coefficients of the corresponding terms on both sides of the equation to find the value of $k$ .
The coefficient of $(x-3)$ in the given function is $\frac{1}{2}$ , and the coefficient of $(x-d)$ in the general form is $k$ . Therefore, we have $\frac{1}{2} = k$

STEP 4

So, the value of $k$ is $\frac{1}{2}$ .
The values of $a$ , $k$ , $d$ , and $c$ are $a=-3$ , $k=\frac{1}{2}$ , $d=3$ , and $c=1$ .

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