Graphing a Linear Function with Two Variables: Exploring y = (x + p) + q

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In summary, the function f(x) = (x + p) + q can be simplified to f(x) = x + c, where c = p + q. This represents a straight line with a slope of 1 and a y-intercept of c. The equation is similar to y = mx + c, and the right side can also be written as (x + p) + q, representing a horizontal and vertical translation of y = x.
  • #1
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Homework Statement


I am not sure how to graph the function

f(x)=(x+p)+q

Homework Equations

The Attempt at a Solution



When x=0 y=p+q
if y=0 x=-q-p ?

what shape would this give??[/B]
 
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  • #2
lola2000 said:

Homework Statement


I am not sure how to graph the function

f(x)=(x+p)+q

Homework Equations

The Attempt at a Solution



When x=0 y=p+q
if y=0 x=-q-p ?

what shape would this give??[/B]
f(x) = (x + p) + q can also be written as f(x) = x + (p + q)
No as p and q are both constants, let:
p + q = c
Sp, we get f(x) = x + c
This is similar to the equation y = mx + c. What does this equation stand for?
 
  • #3
siddharth23 said:
f(x) = (x + p) + q can also be written as f(x) = x + (p + q)
No as p and q are both constants, let:
p + q = c
Sp, we get f(x) = x + c
This is similar to the equation y = mx + c. What does this equation stand for?


So it will just be a straight line upwards with a gradient of 1 and y intercept of p+q?
 
  • #4
lola2000 said:
f(x)=(x+p)+q
This is nothing more than a straight line whose slope is 1 and whose y-intercept is p + q.

The only reason I can think of for writing the right side as (x + p) + q is to get you to recognize this as a horizontal translation and a vertical translation of the graph of y = x.
 
  • #5
lola2000 said:
So it will just be a straight line upwards with a gradient of 1 and y intercept of p+q?
Yes!
 

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