Question

The graph of f(x) = |x| is transformed to g(x) = [X + 11-7. On which interval is the function decreasing?

Answer 1

The interval of the decreasing function is (-∞ , -1) ⇒ g(x)

The interval of the decreasing function is (-∞ , 0) ⇒ f(x)

Explanation:

* Lets explain how to solve it

- Decreasing function means a function with a graph that moves

downward as it is followed from left to right.

- For example, any line with a negative slope is decreasing function

- Lets look to the attached graph to understand the meaning of the

decreasing function

∵ f(x) = IxI ⇒ green graph

∵ g(x) = Ix + 1I - 7 ⇒ purple graph

- From the graph f(x) translated 1 unit to the left and 7 units down to

form g(x)

- The domains of f(x) and g(x) are all real numbers {x : x ∈ R}

- The range of f(x) is {y : y ≥ 0}

- The range of g(x) is {y : y ≥ -7}

# For f(x)

- The slope of the green line from (-∞ , 0) is negative

- The slope of the green line from (0 , ∞) is positive

# For g(x)

- The slope of the purple line from (-∞ , -1) is negative

- The slope of the purple line from (-1 , ∞) is positive

∵ The line with negative slope represent decreasing function

∴ The interval of the decreasing function is (-∞ , -1) ⇒ g(x)

∴ The interval of the decreasing function is (-∞ , 0) ⇒ f(x)