Representations of Functions: Sketch the Graph from a Verbal Description

Creating a table from a verbal descriptionDetermine whether the table represents a functionIs the graph an example of a function?Matching a graph to a functionMatching a graph to a tableMatching a table to a function
Question 1

Given that Y is a function of X that matches any value of 3 times X

Choose the appropriate graph to describe the function

Question 2

Given that Y is a function of X that matches any value of4 times X

Choose the appropriate graph to describe the function

Question 3

Y is a function of X that matches 5 times X .

Which graph represents the function described above?

Question 4

Since Y is a function of X that matches every value of X where the number is greater by 3

Circle the appropriate graph to describe the function

Question 5

Y is a function of X that matches every value of X where the number is greater by 5.

Which graph describes the function?

Examples with solutions for Representations of Functions: Sketch the Graph from a Verbal Description

Exercise #1

Given that Y is a function of X that matches any value of 3 times X

Choose the appropriate graph to describe the function

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Identify the given function Y=3X Y = 3X .
  • Recall that the equation describes a straight line with a slope m=3 m = 3 and y-intercept b=0 b = 0 .
  • Plot the graph as a line through the origin (0,0), rising 3 units for every 1 unit it runs.
  • Analyze each provided graph to find the graph that matches this description.

Given these steps, start plotting the graph from the origin. The slope of 3 implies a steep line where for each unit moved horizontally (to the right), the line moves three units vertically (upwards).

Examining the graphical choices:

  • Option 1 correctly represents a line with slope 3 through (0,0).

Therefore, the graph that describes the function Y=3X Y = 3X is choice Option 1, which matches the linear equation characteristics.

Answer

–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111333666000

Exercise #2

Given that Y is a function of X that matches any value of4 times X

Choose the appropriate graph to describe the function

Video Solution

Step-by-Step Solution

To solve this problem, we need to graph the function Y=4X Y = 4X . Analyzing it, we recognize:

  • This is a linear function in the form Y=mX+b Y = mX + b , where m=4 m = 4 (slope) and b=0 b = 0 (y-intercept).
  • The line passes through the origin, (0,0), because b=0 b = 0 .
  • For a slope of 4, each unit increase in X X results in a 4-unit increase in Y Y .

We look for a graph showing a straight line through (0,0), with slope 4, represented as a steep incline upwards along the coordinate plane.

From the provided choices, we select the graph with a linear function that passes through the origin at an angle indicating a slope of 4, leading us to choice 2, the correct representation.

Thus, the correct graph of the function Y=4X Y = 4X is the one depicted in choice 2.

Answer

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Exercise #3

Y is a function of X that matches 5 times X .

Which graph represents the function described above?

Video Solution

Step-by-Step Solution

To find the correct graph, follow these steps:

  • Step 1: Identify the equation Y=5X Y = 5X as a linear function with a slope of 5 and a y-intercept of 0.
  • Step 2: Locate the graph that depicts a line passing through the origin (0,0) with a steep rise indicating a slope of 5.
  • Step 3: Examine the given choices to see which one fits this description.

After examining the choices, the appropriate graph shows a line passing through the origin with the correct slope of 5. The correct representation of the function Y=5X Y = 5X is:

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Answer

–17–17–17–16–16–16–15–15–15–14–14–14–13–13–13–12–12–12–11–11–11–10–10–10–9–9–9–8–8–8–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999101010–15–15–15–10–10–10–5–5–5

Exercise #4

Since Y is a function of X that matches every value of X where the number is greater by 3

Circle the appropriate graph to describe the function

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Recognize the function Y=X+3 Y = X + 3 as a linear function.
  • Step 2: Identify that it has a slope of 1 and a y-intercept at Y=3 Y = 3 .
  • Step 3: Look for a graph that represents a line with the described characteristics.

Let's apply these steps to solve the problem:
Step 1: The function Y=X+3 Y = X + 3 suggests a linear relationship.
Step 2: With a slope of 1, the graph rises 1 unit vertically for every 1 unit horizontally. The y-intercept is 3, meaning the line passes through the point (0,3) (0, 3) .
Step 3: On inspecting the provided choices, identify the graph with the line intersecting the y-axis at 3 and having a slope of 1.

Therefore, the graph that represents the function Y=X+3 Y = X + 3 is the one given by: choice 1.

Answer

–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111–1–1–1111222333444555666777000

Exercise #5

Y is a function of X that matches every value of X where the number is greater by 5.

Which graph describes the function?

Video Solution

Step-by-Step Solution

To solve this problem, we will sketch the graph of the function Y=X+5 Y = X + 5 .

  • Step 1: Identify key points by calculating a few points for the graph:
    For X=0 X = 0 , Y=0+5=5 Y = 0 + 5 = 5 .
    For X=1 X = 1 , Y=1+5=6 Y = 1 + 5 = 6 .
    For X=2 X = 2 , Y=2+5=7 Y = 2 + 5 = 7 .
  • Step 2: Plot these points on a Cartesian plane.
    - The points (0,5)(0, 5), (1,6)(1, 6), and (2,7)(2, 7) all lie on the line with a slope of 1.
  • Step 3: Draw the straight line through these points extending in both directions.

As Y=X+5 Y = X + 5 represents a line with a slope of 1 and y-intercept of 5, the line will pass through all these points. Comparing this to the provided graph choices, select the graph with positive slope and y-intercept at 5.

The correct graph is choice 2, which shows a line with a slope of 1 and intercepting the y-axis precisely at 5.

Therefore, the graph that describes the function Y=X+5 Y = X + 5 correctly is choice 2.

Answer

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Question 1

Since Y is a function of X that matches any value of X a number less than it for 8

Circle the appropriate graph to describe the function

Question 2

Since Y is a function of X that matches any value of \( \frac{1}{5} \) times X

Choose the appropriate graph to describe the function

Question 3

Y is a function of X that matches every value of X plus 4.

Choose the appropriate graph to describe the function.

Exercise #6

Since Y is a function of X that matches any value of X a number less than it for 8

Circle the appropriate graph to describe the function

Video Solution

Step-by-Step Solution

We need to determine which graph represents the function Y=f(X) Y = f(X) where Y Y is strictly less than 8 for all X X . A key indication is that the function should be a horizontal line or region that does not reach or exceed the line Y=8 Y = 8 .

Reviewing the provided options, look for a graph that closely aligns with being constantly below the line Y=8 Y = 8 . Given the descriptions, a horizontal line at Y=7 Y = 7 or Y=6 Y = 6 would work since it satisfies the inequality Y<8 Y < 8 regardless of the X X values.

Option 4 clear depicts a line where all Y Y -values are indeed less than 8. The graph shows a continuous horizontal segment that stays consistently below 8.

Thus, the graph that correctly describes this function is the one in Choice 4.

Answer

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Exercise #7

Since Y is a function of X that matches any value of 15 \frac{1}{5} times X

Choose the appropriate graph to describe the function

Video Solution

Answer

–15–15–15–10–10–10–5–5–5–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222000

Exercise #8

Y is a function of X that matches every value of X plus 4.

Choose the appropriate graph to describe the function.

Video Solution

Answer

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