Identify Function From Verbal Description Worksheet

6 problems

To identify a function from a verbal description, translate the described relationship between variables into a mathematical expression. This involves recognizing keywords that indicate operations (like "sum" for addition or "product" for multiplication) and understanding how the variables interact. Practicing with an identify function from verbal description worksheet can help reinforce these skills.

Algebra 2
Exponential Functions

How Will This Worksheet on "Identify Function from Verbal Description" Benefit Your Student's Learning?

• Helps students turn real-life situations into math problems, boosting critical thinking.
• Improves the ability to break down and understand verbal information accurately.
• Enhances skills in explaining mathematical ideas both verbally and in writing.
• Deepens the understanding of functions by connecting descriptions to mathematical expressions.
• Develops the ability to logically connect verbal information to mathematical concepts.

How to Identify Function from Verbal Description?

• Identify whether the function describes linear or exponential growth based on the verbal description.
• Note the initial condition provided, which will serve as the starting point for identifying the function rule.
• Recognize the given factor by which the function increases over each interval, indicating how the function's value changes with each step.
• Use the initial condition and the growth factor to express the function as an exponential equation, capturing the described behavior.

Solved Example

Q. A function $f(x)$ increases by $6$ over every unit interval in $x$ and $f(0) = 0$.$\newline$Which could be a function rule for $f(x)$?$\newline$Choices:$\newline$(A) $f(x) = 6x$$\newline$(B) $f(x) = 6^x$$\newline$(C) $f(x) = \frac{1}{6^x}$$\newline$(D) $f(x) = \frac{x}{6}$
Solution:
1. Identify Function Type: Determine the type of function based on the rate of increase. Since $f(x)$ increases by $6$ over every unit interval in $x$, this suggests a constant rate of change, which is characteristic of a linear function.
2. General Form of Linear Function: Write the general form of a linear function.$\newline$The general form of a linear function is $f(x) = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
3. Find Slope: Use the given information to find the slope $m$. The function increases by $6$ for each unit increase in $x$, so the slope $m$ is $6$.
4. Find Y-Intercept: Use the given information to find the y-intercept $b$. Since $f(0) = 0$, when $x = 0$, $f(x)$ should equal $0$. Plugging these values into the general form gives us $0 = m(0) + b$, which simplifies to $b = 0$.
5. Write Specific Function Rule: Write the specific function rule for $f(x)$. With $m = 6$ and $b = 0$, the function rule is $f(x) = 6x$.

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