How Does Shifting Affect the Function f(x)?

In summary, absolute value is a mathematical concept that measures the distance of a number from zero on a number line and is always positive. To solve absolute value problems, you need to isolate the expression and consider positive and negative cases. It has many real-world applications in fields such as physics, engineering, finance, and computer science. When multiplied or divided by a positive number, it remains unchanged, but when multiplied or divided by a negative number, it becomes negative. The graph of the absolute value function is a V-shaped graph with a slope of 1 on both sides of the vertex, representing the rate of change of the function.
  • #1
MathExpert
6
0
If

f(x+a1) = x^2 + x + 2



then what is

f(x-a)



Please help!
 
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  • #2
this seems to mean that f(anything +a) = (anything)^2 + anything + 2.

so here you have to write f(x-a) as f(something + a), and then apply the polynomial above to th something. what would the something be?
 
  • #3
1. What does this have to do with absolute value?

2. What is the difference between a and a1? What do they mean?
 

What is absolute value?

Absolute value is a mathematical concept that represents the distance of a number from zero on a number line. It is always a positive value, regardless of the sign of the number.

How do I solve absolute value problems?

To solve an absolute value problem, you need to isolate the absolute value expression and then consider two cases: one where the value inside the absolute value is positive, and one where it is negative. You can then solve for both cases and get two solutions.

What are some real-world applications of absolute value?

Absolute value is commonly used in physics and engineering to represent magnitude, distance, and error. It is also used in finance to represent profit and loss, and in computer science to represent the difference between two values.

What happens when the absolute value of a number is multiplied or divided by another number?

Multiplying or dividing an absolute value by a positive number will not change its value, while multiplying or dividing by a negative number will result in the absolute value becoming negative. This is because the absolute value strips away the sign of a number.

How does the absolute value function relate to the graph of a line?

The graph of the absolute value function is a V-shaped graph, with the vertex at the origin. It is symmetric about the y-axis and has a slope of 1 on both sides of the vertex. This slope represents the rate of change of the function at any point on the graph.

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