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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 fx ax k1n c What does the graph tell you about the value of a in this functio class=

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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 [tex]f(x) = a(x + k)^{\frac{1}{n}} + c[/tex].

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

The parent function of given graph is [tex]\sqrt2[/tex]

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

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

⇒ [tex]5=a(-4+5)^{\frac{1}{2}}+2[/tex]

⇒ [tex]5-2=a[/tex]

⇒ 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:

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

The parent function of f(x) is:

[tex]\mathbf{y =x^\frac{1}{2}}[/tex]

So, by comparison:

[tex]\mathbf{n =2}[/tex]

The function becomes:

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

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

So, we have:

[tex]\mathbf{(k,c) = (-5,2)}[/tex]

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

So, the function becomes

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

From the graph, we have the following point;

[tex]\mathbf{(x,y) = (-4,5)}[/tex]

So, the function becomes

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

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

Subtract 2 from both sides

[tex]\mathbf{3=a(-9)^\frac{1}{2}}[/tex]

Square both sides

[tex]\mathbf{9=a(-9)}[/tex]

Divide both sides by -9

[tex]\mathbf{-1=a}[/tex]

So, we have:

[tex]\mathbf{a = -1}[/tex]

-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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