What are 3 completed examples for functions?

1 answer:

3 0

Example 1

Write y = x2 + 4x + 1 using function notation and evaluate the function at x = 3.

Solution

Given, y = x2 + 4x + 1

By applying function notation, we get

f(x) = x2 + 4x + 1

Evaluation:

Substitute x with 3

f (3) = 32 + 4 × 3 + 1 = 9 + 12 + 1 = 22

Example 2

Evaluate the function f(x) = 3(2x+1) when x = 4.

Solution

Plug x = 4 in the function f(x).

f (4) = 3[2(4) + 1]

f (4) = 3[8 + 1]

f (4) = 3 x 9

f (4) = 27

Example 3

Write the function y = 2x2 + 4x – 3 in function notation and find f (2a + 3).

Solution

y = 2x2 + 4x – 3 ⟹ f (x) = 2x2 + 4x – 3

Substitute x with (2a + 3).

f (2a + 3) = 2(2a + 3)2 + 4(2a + 3) – 3

= 2(4a2 + 12a + 9) + 8a + 12 – 3
= 8a2 + 24a + 18 + 8a + 12 – 3
= 8a2 + 32a + 27

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Which function f (x) , graphed below, or g (x) , whose equation is g (x) = 3 cos 1/4 (x + x/3) + 2, has the largest maximum and

Leya [2.2K]

Answer:

g(x), and the maximum is 5

Step-by-step explanation:

for given function f(x), the maximum can be seen from the shown graph i.e. 2

But for the function g(x), maximum needs to be calculated.

Given function :

g (x) = 3 cos 1/4 (x + x/3) + 2

let x=0 (as cosine is a periodic function and has maximum value of 1 at 0 angle)

g(x)= 3 cos1/4(0 + 0) +2