is the algebraic representation for an exponential function
Step-by-step explanation:
Given:
f(x + 1) = 4.f(x)
f(3) = 16
To Find:
Algebraic representation for an exponential function=?
Solution:
From the formula f(x+n) = f(x)
when n= 1, x= 3
f(3+1)= 4(1)f(3)
f(4)= 4f(3)
Substituting the value of f(3)
f(4)= 4f(3)
f(4)= 4 x 16
f(4)= 64
f(4)=
f (5) = x 16
f (5) = x
f(5)=
Similarly,
F(6) =
Hence,
Answer:
<em>Observe attached image</em>
<em>Function zeros:</em>
(3, 0), (5, 0)
<em>Vertex:</em>
(4, 2)
<em>Axis of symmetry:</em>
<em></em>
Step-by-step explanation:
<u>First factorize the function</u>
<em>Take -2 as a common factor.</em>
<em>Now factor the expression </em>
You must find two numbers that when you add them, obtain the result -8 and multiplying those numbers results in 15.
These numbers are -5 and -3
Then we can factor the expression in the following way:
<em><u>The quadratic function cuts the x-axis at </u></em><em>x = 3 and at x = 5.</em>
Now we find the coordinates of the vertex.
For a function of the form the x coordinate of its vertex is:
In the function
<u>Then the vertice is:</u>
The y coordinate of the symmetry axis is
The axis of symmetry is a vertical line that cuts the parabola in two equal halves. This axis of symmetry always passes through the vertex.
<u>Then the axis of symmetry is the line</u>
<u>The solutions and the vertice written as ordered pairs are:</u>
<em>Function zeros:</em>
(3, 0), (5, 0)
<em>Vertex:</em>
(4, 2)
