Question

Given \(f(x) = |x|\), after performing the following transformations: shift to the left 10 units, compress vertically by a factor of \(1/51\), and shift downward 11 units, the new function \(g(x)\) is: a) \(g(x) = \left|\frac{x}{51} - 10\right| - 11\) b) \(g(x) = \left|\frac{x}{51} + 10\right| - 11\) c) \(g(x) = \left|\frac{x}{51} - 10\right| + 11\) d) \(g(x) = \left|\frac{x}{51} + 10\right| + 11\)

Answer 1

The new function (g(x)) after applying the given transformations to the original function (f(x) = |x|) is (g(x) = |(x/51) - 10| - 11).

Option (a) is true.

Explanation:

To determine the new function (g(x)) after applying the given transformations to the original function (f(x) = |x|), we need to follow these steps:

Shift to the left 10 units:

This can be done by replacing (x) with (x + 10).

Compress vertically by a factor of (1/51):

This can be done by multiplying the entire function by (1/51).

Shift downward 11 units:

This can be done by subtracting 11 from the entire function.

Applying these transformations to the original function (f(x) = |x|), we get:

(f(x) = |x|) is (g(x) = |(x/51) - 10| - 11).

Thus,

Option (a) is true.