Function Analysis: Determining Behavior When Dividing by -1

Question

Determine whether the function is increasing, decreasing, or constant. For each function check your answers with a graph or table:

Each number is divided by (−1) (-1) .

Video Solution

Solution Steps

00:11 Is the function increasing, decreasing, or staying constant?
00:16 First, let's draw the graph of the function.
00:22 We'll substitute some X values to find their matching Y values.
00:39 Now, let's try some negative X values to see the graph's left side.
00:46 We observe that the graph is always decreasing.
00:50 And that's how we solve this question!

Step-by-Step Solution

The function is:

f(x)=x−1 f(x)=\frac{x}{-1}

Let's start by assuming that x equals 0:

f(0)=0−1=0 f(0)=\frac{0}{-1}=0

Now let's assume that x equals 1:

f(1)=1−1=−1 f(1)=\frac{1}{-1}=-1

Now let's assume that x equals 2:

f(−1)=−1−1=1 f(-1)=\frac{-1}{-1}=1

Let's plot all the points on the function graph:

–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666–1–1–1111222333444000

We see that we got a decreasing function.

Answer

Decreasing

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Increasing and Decreasing Intervals (Functions) Functions for Seventh Grade Increasing functions Decreasing function Constant Function Decreasing Interval of a function Increasing Intervals of a function

Question Types

Increasing and Decreasing Intervals of a Function: Identifying increase and decrease from a verbal description of the function