Math Is Fun Forum

nycguitarguy

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 571

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).

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The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.

Dr. David Jeremiah

Bob

Administrator

Registered: 2010-06-20

Posts: 10,212

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

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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: 10,212

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

nycguitarguy

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 571

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.

---

The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.

Dr. David Jeremiah

nycguitarguy

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 571

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.

---

The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.

Dr. David Jeremiah

nycguitarguy

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 571

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.

---

The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.

Dr. David Jeremiah