# Composite function and characteristics of a graph

1. Given f(x) = 4x^2 - 3 and g(x) = 5 - 1/2x^2. Find the following expressions. Simplify your answer for all solutions.

(a) (f o g)(4)

(b) (g o f)(2)

(c) (f o f)(1)

(d) (g o g)(0)

2. For the given equation, list the intercepts and test for symmetry. x^2 + y - 16 = 0

A. What are the intercept(s)? Write as an ordered pair or there are no intercepts.

B. Is the graph of the equation symmetric with respect to the x-axis?

Is the graph of the equation symmetric with respect to the y-axis?

Is the graph of the equation symmetric with respect to the origin?

https://brainmass.com/math/basic-algebra/composite-function-characteristics-graph-596613

#### Solution Preview

1.

F(x) = 4x^2 - 3

g(x) = 5 - x^2/2

a.

Fog(4) = F(g(4)) = F(5 - 4^2/2) = F(5 - 8) = F(-3) = 4*(-3)^2 - 3 = 33

b.

goF(2) ...

#### Solution Summary

In this solution, composite function values and characteristics of a graph for a given function are estimated.

5 Simple Algebra and Function Questions

See the attached file.

1. Determine whether the graph of y = 3 + x2 is symmetric with respect to

the x-axis, the y-axis, or the origin.

2. A salesperson earns a base salary of $2,000 per month and a commission

of 5% on the amount of sales made. If the salesperson has a paycheck of

$3,006 for one month, what was the amount of sales for the month?

Solution: (correct?)

2,000 + .05(x) = 3006

2000 + .05(x) -2000 = 3006 - 2000

.05x = 1006

.05x / .05 = 1006 / .05

X = 20,120

The salesperson had $20,120 in sales for the month.

(2000+.05(20,120) = 3,006

3. For x values in what interval (s) is the function increasing?

4. a. Given f (x) = 4/x2 and g(x) = 3 - 2x, find the composite function

(f o g)(x) and simplify.

b. Write the equation for a function that has a graph with the

given characteristics.

The shape of y = |x| but stretched vertically by a factor of 2 and shifted right 3 units.

5. a. Solve for n: 2(n - 1) = 3(n + 5)

Solution:

b. Find the zero of the function f(x) = 8 - 2x

Solution: ?

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