Subtracting inside the functionf(x) = 2(x -3)²
moves right
To subtract inside the function f(x) = 2(x -3)², we can perform the subtraction inside the parentheses first and then continue simplifying the expression. For example, suppose we want to subtract 4 from the input of the function, i.e., evaluate f(x – 4):
f(x – 4) = 2((x – 4) – 3)² (substituting x – 4 for x)
= 2(x – 7)² (simplifying inside the parentheses)
Alternatively, we can distribute the 2 and use the property that if f(x) = 2x², then f(ax + b) = 2(ax + b)², where a and b are constants:
f(x – 4) = 2(x – 4 – 3)² (substituting x – 4 for x and simplifying inside the parentheses)
= 2(x – 7)² (simplifying)
= 2x² – 28x + 98 (expanding using the square of a binomial formula)
= f(x) – 28(x – 7) (expressing the result in terms of f(x))
In this second method, we can see that subtracting 4 inside the function is equivalent to subtracting 28 from the output of the function, which is a linear transformation of the graph of f(x).
More Answers:
How the Intermediate Value Theorem Works to Find Solutions to EquationsUnderstanding the Fundamental Concept of Continuity in Mathematics: Definition and Conditions Explained
Mastering Calculus: Four Effective Methods to Evaluate Limits