Final answer:
To determine if the functions f(x)=∣x+3∣ and g(x)=∣∣x∣+3∣ are equivalent, we can graph them and compare. The graphs of the two functions are not equivalent, as f(x) has a corner point at (0, 3), while g(x) does not have a corner point.
Step-by-step explanation:
The functions f(x)=∣x+3∣ and g(x)=∣∣x∣+3∣ can be graphed to determine if they are equivalent.
To graph f(x)=∣x+3∣, we start by determining the key points on the graph. When x is negative, the absolute value of x+3 can be simplified to -(x+3), which means the graph will be a downward-sloping line. When x is positive, the absolute value of x+3 can be simplified to (x+3), which means the graph will be an upward-sloping line.
To graph g(x)=∣∣x∣+3∣, we start by determining the key points as well. When x is negative, the absolute value of x+3 can be simplified to -(x+3), which means the graph will be a downward-sloping line. When x is positive, the absolute value of x+3 can be simplified to (x+3), which means the graph will be an upward-sloping line.
Comparing the graphs of f(x) and g(x), we can see that they are not equivalent. The key difference is that f(x) has a corner point at (0, 3), while g(x) does not have a corner point.