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The graph shown below expresses a radical function that can be written in the form f(x) = a(x + k)^1/n + c. What does the graph tell you about the value of a in this function?

The graph shown below expresses a radical function that can be written in the form f(x) = a(x + k) 1/n + c. What does the graph tell you about the value of a in class=

Verified Answer :

Answer:

The value of a is 3

Step-by-step explanation:

Given the graph which shows a radical function that can be written in the form \(f(x) = a(x + k)^{\frac{1}{n}} + c\).

we have to tell about the value of a in this function below.

The parent function of given graph is \(\sqrt2\)

As the given function of graph is the square root function which shows

n=2 and the vertex is (-k,c)

From the graph it is clear that (-5,2)

⇒ k=5, c=2

Now, we have to find the value of a

Now, graph passes through the point (-4,5)

Hence, put all the values in order to find the value of a

\(f(x) = a(x + k)^{\frac{1}{n}} + c\)

⇒ \(5=a(-4+5)^{\frac{1}{2}}+2\)

⇒ \(5-2=a\)

⇒ a=3

The value of a is 3

MrRoyal

Graphs can be used to represent functions

The value of a is less than 0.

The function is given as:

\(\mathbf{f(x)=a(x + k)^\frac{1}{n} + c}\)

The parent function of f(x) is:

\(\mathbf{y =x^\frac{1}{2}}\)

So, by comparison:

\(\mathbf{n =2}\)

The function becomes:

\(\mathbf{f(x)=a(x + k)^\frac{1}{2} + c}\)

Next, we identify the vertex (in this case, the vertex is the minimum point on the graph)

So, we have:

\(\mathbf{(k,c) = (-5,2)}\)

Substitute these values in \(\mathbf{f(x)=a(x + k)^\frac{1}{2} + c}\)

So, the function becomes

\(\mathbf{f(x)=a(x -5)^\frac{1}{2} + 2}\)

From the graph, we have the following point;

\(\mathbf{(x,y) = (-4,5)}\)

So, the function becomes

\(\mathbf{5=a(-4 -5)^\frac{1}{2} + 2}\)

\(\mathbf{5=a(-9)^\frac{1}{2} + 2}\)

Subtract 2 from both sides

\(\mathbf{3=a(-9)^\frac{1}{2}}\)

Square both sides

\(\mathbf{9=a(-9)}\)

Divide both sides by -9

\(\mathbf{-1=a}\)

So, we have:

\(\mathbf{a = -1}\)

-1 is less than 0.

Hence, the value of a is less than 0.

Read more about graphs and functions at:

https://brainly.com/question/11804653

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