Question

The function f(x) = −2x + 5 is changed to f(x) = 2x + 5. Which describes the effect of the change on the graph of the original function? A) The line will be steeper. B) The line will be less steep. C) Line changes from increasing to decreasing. D) Line changes from decreasing to increasing.

Answer 1

As the Slopes of both the Functions are Same, They are Equally Steep.

⇒ Option A and Option B cannot be the Answers

As the First Line Slope is Negative and As the Second Line Slope is Positive, The Line Changes from Decreasing to Increasing

⇒ Option D is the Answer

Answer 2

D) Line changes from decreasing to increasing

Explanation:

Since, we know that,

A line with positive slope is increasing while with negative slope is decreasing,

Here, the given line,

f(x) = -2x + 5

After transforming, new line,

g(x) = 2x + 5

∵ slope of f(x) is negative and slope of g(x) is positive

⇒ f(x) is decreasing and g(x) is increasing,

⇒ Line changes from decreasing to increasing

Also, if the absolute value of the slope is increasing then line gets steeper.

Note : Steepness : closeness of a line with y-axis.

∵ |-2| = |2|,

That is, there is no affect in steepness.

Hence, OPTION D is correct.