MAT1510 ASSIGNMENT 2 2025

MAT1510
ASSIGNMENT 2
2025

, QUESTION 1


1.1).


x2 if x<1
g(x) = { 1 if 1≤x<2
|x| if 2≤x<5
5 if x≥5




1.2).


A function is a mapping that provides a single output value to each input value
in its domain. While g(x)is defined piecewise, there is only one output for a
given input x.

, 1.3).


3
g(1) = g ( ) ⇒ (1)2 = 1
2
1=1


3 3
Since g(1) = g ( ) but 1 ≠ , then g(x) is not one − to − one
2 2


1.4).


x2 + 4 if x<1
f(x) = { 1 + 4 if 1≤x<2
|x| + 4 if 2≤x<5
5+4 if x≥5
x2 + 4 if x<1
f(x) = { 5 if 1≤x<2
|x| + 4 if 2≤x<5
9 if x≥5




QUESTION 2


2.1).
f(x) = |x|


Stretching horizontall by a factor of 2:
x
f(x) = | |
2


Shifting the graph horizontally by 6 units to the left:
x+6
f(x) = | |
2