Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Random Questions About Two Functions

Given f(x) = (x^2 + 2)/(x + 4) and g(x) = 2x/(x - 2), answer the following questions.

A. The point (1, 3/5) lies on the graph of which function?

B. If x = 4, what if g(x)? What point is on the graph of g?

C. What is the domain of f and g?

D. If f(x) = 1/2 and g(x) = 1, what is x for both functions?

E. Graph the function of f. Graph the function of g.

F. What is the range of f? What is the range of g?

G. List the x and y intercepts, if any, of the graph of f and graph of g.

H. Find f(a + b) and g(a - b).

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Random Questions About Two Functions

If you sub. in those x and y values find out in which equation they fit.

I've got to go out now.

I'll look at the rest when I get back.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Random Questions About Two Functions

Given f(x) = (x^2 + 2)/(x + 4) and g(x) = 2x/(x - 2), answer the following questions.

A. The point (1, 3/5) lies on the graph of which function?

Plug x=1 into f and g
see which one gives you 3/5 for the answer

B. If x = 4, what if g(x)? What point is on the graph of g?

Plug x=4 into g
See what g(4) equals
This is y
Point on g is (4,g(4))

C. What is the domain of f and g?

Domains are different for f and g
f: solve x+4=0; everything else is domain
g: solve x-2=0: everything else is domain

D. If f(x) = 1/2 and g(x) = 1, what is x for both functions?

f: set (x^2 + 2)/(x + 4) = 1/2 and solve
g: set 2x/(x - 2), = 1 and solve

E. Graph the function of f. Graph the function of g.

graph vertical asymptotes
use the rules to find horizontal asymptotes
plot intercepts
make T-chart
graph a bunch of other points
then draw graph

F. What is the range of f? What is the range of g?

like Bob said: look at the graph for the range
(you already have the domains)

G. List the x and y intercepts, if any, of the graph of f and graph of g.

y-int: set x=0 and solve
x-int: set y=0 and solve

H. Find f(a + b) and g(a - b).

plug a+b in for each x in f
plug a-b in for each x in g
simplify if you can

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Random Questions About Two Functions

Fully agree!

I find the following really useful:

https://www.mathsisfun.com/data/function-grapher.php

The default set of x and y values does not show fully what these functions look like in graph form.  You need to zoom out. You can also drag to move to a different part of the axes.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Random Questions About Two Functions

If you sub. in those x and y values find out in which equation they fit.

I've got to go out now.

I'll look at the rest when I get back.

Bob

I will play around with set of questions later on. It looks like fun.

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Random Questions About Two Functions

Given f(x) = (x^2 + 2)/(x + 4) and g(x) = 2x/(x - 2), answer the following questions.

A. The point (1, 3/5) lies on the graph of which function?

Plug x=1 into f and g
see which one gives you 3/5 for the answer

B. If x = 4, what if g(x)? What point is on the graph of g?

Plug x=4 into g
See what g(4) equals
This is y
Point on g is (4,g(4))

C. What is the domain of f and g?

Domains are different for f and g
f: solve x+4=0; everything else is domain
g: solve x-2=0: everything else is domain

D. If f(x) = 1/2 and g(x) = 1, what is x for both functions?

f: set (x^2 + 2)/(x + 4) = 1/2 and solve
g: set 2x/(x - 2), = 1 and solve

E. Graph the function of f. Graph the function of g.

graph vertical asymptotes
use the rules to find horizontal asymptotes
plot intercepts
make T-chart
graph a bunch of other points
then draw graph

F. What is the range of f? What is the range of g?

like Bob said: look at the graph for the range
(you already have the domains)

G. List the x and y intercepts, if any, of the graph of f and graph of g.

y-int: set x=0 and solve
x-int: set y=0 and solve

H. Find f(a + b) and g(a - b).

plug a+b in for each x in f
plug a-b in for each x in g
simplify if you can

Copy. Thank you for your time and effort. Wish I had more time to spend hours with math on a daily basis.

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Random Questions About Two Functions

Fully agree!

I find the following really useful:

https://www.mathsisfun.com/data/function-grapher.php

The default set of x and y values does not show fully what these functions look like in graph form.  You need to zoom out. You can also drag to move to a different part of the axes.

Bob

Thank you for the link. Every reply a little more than the previous.