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

Identifying which domain is applicable for the described functionMatching the graph to the storyDetermine whether or not it is possible to create the functionFinding Increasing or Decreasing Domains
Question 1

Determine whether the function described below is increasing, decreasing, or constant.

Each number is multiplied by the same number.

Question 2

Determine whether the function described below is increasing, decreasing, or constant:

Each number is multiplied by the same number with different signs.

Question 3

Determine whether the function is increasing, decreasing, or constant. Check your answer with a graph or table.

For each number corresponding to the number \( -1 \).

Question 4

Determine whether the function is increasing, decreasing, or constant. For each function, check your answers using a graph or a table:
Each number is multiplied by 0.5.

Question 5

Determine whether the function is increasing, decreasing, or constant. For each function check your answers using a graph or a table. Each number is multiplied by itself three times.

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

Exercise #1

Determine whether the function described below is increasing, decreasing, or constant.

Each number is multiplied by the same number.

Video Solution

Step-by-Step Solution

The function is:

f(x)=x2 f(x)=x^2

Let's start with x equal to 0:

f(0)=02=0 f(0)=0^2=0

Now let's assume x is equal to 1:

f(1)=12=1 f(1)=1^2=1

Now let's assume x is equal to 2:

f(2)=22=4 f(2)=2^2=4

Now let's assume x is equal to minus 1:

f(−1)=(−1)2=1 f(-1)=(-1)^2=1

Now let's assume x is equal to minus 2:

f(−2)=(−2)2=4 f(-2)=(-2)^2=4

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 can see that we got a function that is both increasing and decreasing.

Answer

Increasing and decreasing

Exercise #2

Determine whether the function described below is increasing, decreasing, or constant:

Each number is multiplied by the same number with different signs.

Video Solution

Step-by-Step Solution

The function is:

f(x)=x×(−x) f(x)=x\times(-x)

Let's start by assuming thatx x equals 0:

f(0)=0×0=0 f(0)=0\times0=0

Now let's assume that x x equals 1:

f(1)=1×−1=−1 f(1)=1\times-1=-1

Now let's assume that x x equals -1:

f(−1)=(−1)×(−1)=1 f(-1)=(-1)\times(-1)=1

Now let's assume that x x equals 2:

f(2)=2×(−2)=−4 f(2)=2\times(-2)=-4

Now let's assume that x x equals -2:

f(−2)=(−2)×(−2)=4 f(-2)=(-2)\times(-2)=4

Finally, let's plot all of the points on a graph:

–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111000

We can see that the function both increases and decreases.

Answer

Increasing and decreasing

Exercise #3

Determine whether the function is increasing, decreasing, or constant. Check your answer with a graph or table.

For each number corresponding to the number −1 -1 .

Video Solution

Step-by-Step Solution

The function is:

f(x)=x−1 f(x)=x-1

Let's start with x equal to 0:

f(0)=0−1=−1 f(0)=0-1=-1

Now let's assume x is equal to 1:

f(1)=1−1=0 f(1)=1-1=0

Now let's assume x is equal to 2:

f(2)=2−1=1 f(2)=2-1=1

Now let's assume x is equal to minus 1:

f(−1)=(−1)−1=−2 f(-1)=(-1)-1=-2

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

–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666–3–3–3–2–2–2–1–1–1111222000

It appears that the function we obtained is an increasing function.

Answer

Increasing

Exercise #4

Determine whether the function is increasing, decreasing, or constant. For each function, check your answers using a graph or a table:
Each number is multiplied by 0.5.

Video Solution

Step-by-Step Solution

The function is:

f(x)=0.5x f(x)=0.5x

Let's start with x equal to 0:

f(0)=0×0.5=0 f(0)=0\times0.5=0

Now let's assume x is equal to 1:

f(1)=1×0.5=0.5 f(1)=1\times0.5=0.5

Now let's assume x is equal to 2:

f(2)=2×0.5=1 f(2)=2\times0.5=1

Let's record all the data in a table:

X01200.51f(x)Note that the function is always increasing.

Answer

Growing

Exercise #5

Determine whether the function is increasing, decreasing, or constant. For each function check your answers using a graph or a table. Each number is multiplied by itself three times.

Video Solution

Step-by-Step Solution

The function is:

f(x)=xxx f(x)=xxx

Let's start with x equal to 0:

f(0)=0×0×0=0 f(0)=0\times0\times0=0

Now let's assume x is equal to 1:

f(1)=1×1×1=1 f(1)=1\times1\times1=1

Now let's assume x is equal to 2:

f(2)=2×2×2=8 f(2)=2\times2\times2=8

Let's record all the data in a table:

X012018f(x)Note that the function is always increasing.

Answer

Growing

Question 1

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 \( (-1) \).

Question 2

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

For each number, multiply by 0.

Question 3

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

For each number, multiply by\( (-1) \).

Exercise #6

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

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

Exercise #7

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

For each number, multiply by 0.

Video Solution

Step-by-Step Solution

The function is:

f(x)=x×0 f(x)=x\times0

Let's start by assuming that x equals 0:

f(0)=0×0=0 f(0)=0\times0=0

Now let's assume that x equals 1:

f(1)=1×0=0 f(1)=1\times0=0

Now let's assume that x equals -1:

f(−1)=(−1)×0=0 f(-1)=(-1)\times0=0

Now let's assume that x equals 2:

f(2)=2×0=0 f(2)=2\times0=0

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

–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666–3–3–3–2–2–2–1–1–1111222000

We can see that the function we obtained is a constant function.

Answer

Constant

Exercise #8

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

For each number, multiply by(−1) (-1) .

Video Solution

Step-by-Step Solution

The function is:

f(x)=(−1)x f(x)=(-1)x

Let's start by assuming that x equals 0:

f(0)=(−1)×0=0 f(0)=(-1)\times0=0

Now let's assume that x equals minus 1:

f(−1)=(−1)×(−1)=1 f(-1)=(-1)\times(-1)=1

Now let's assume that x equals 1:

f(1)=(−1)×1=−1 f(1)=(-1)\times1=-1

Now let's assume that x equals 2:

f(2)=(−1)×2=−2 f(2)=(-1)\times2=-2

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

–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666–3–3–3–2–2–2–1–1–1111222000

We can see that the function we got is a decreasing function.

Answer

Decreasing