Name That Function Type

What type of function is this?

The Phone Plan: A cell phone company charges a monthly fee of $30 plus $0.10 for every minute used over 500 minutes. Write an equation to represent the total monthly cost (C) for using m minutes (where m > 500).

• Linear

• Absolute Value

• Exponential

• Quadratic

Answer explanation

The total cost C is represented by C = 30 + 0.10(m - 500). This equation is linear because it has a constant rate of change (the $0.10 per minute) and can be expressed in the form y = mx + b.

What Type of Function is This?

Walking for Charity: Sarah is participating in a charity walk. She starts 2 miles from the finish line and walks at a constant pace of 3 miles per hour. Write an equation to represent her distance (d) from the finish line after t hours.

• Linear

• Absolute Value

• Exponential

• Quadratic

Answer explanation

Sarah's distance from the finish line decreases at a constant rate of 3 miles per hour. This relationship can be expressed as a linear equation, making the function linear.

What Type of Function is This?

Cookie Dough Sales: A bakery sells tubs of cookie dough for $8 each. The total revenue (R) the bakery earns is directly proportional to the number of tubs (n) sold. Write an equation to represent the total revenue.

• Linear

• Absolute Value

• Exponential

• Quadratic

Answer explanation

The total revenue (R) is directly proportional to the number of tubs (n) sold, which can be expressed as R = 8n. This is a linear relationship, as it forms a straight line when graphed, making 'Linear' the correct choice.

What Type of Function is This?

Target Practice: In an archery competition, the target has a bullseye at the center. A participant's score is based on how close their arrow lands to the bullseye. If the ideal distance is 0 cm, write an expression that represents the distance (d) of an arrow from the bullseye, regardless of direction.

• Linear

• Absolute Value

• Exponential

• Quadratic

Answer explanation

The distance from the bullseye can be expressed as d = |x|, where x is the distance in any direction. This absolute value function captures the idea of distance, which is always non-negative, making 'Absolute Value' the correct choice.

What Type of Function is This?

Temperature Control: A chemical reaction needs to be maintained at a temperature of 150 degrees Celsius. The reaction is considered unstable if the temperature deviates by more than 5 degrees Celsius from the ideal temperature. Write an inequality using absolute value to represent the acceptable range of temperatures (T) for the reaction.

• Linear

• Absolute Value

• Exponential

• Quadratic

Answer explanation

The acceptable temperature range is represented by the inequality |T - 150| ≤ 5. This form uses absolute value to express the deviation from the ideal temperature, making 'Absolute Value' the correct type of function.

What Type of Function is This?

Manufacturing Error: A machine produces parts with a target length of 25 millimeters. The acceptable error in the length is 0.05 millimeters. Write an absolute value inequality that describes the possible lengths (L) of an acceptable part.

• Linear

• Absolute Value

• Exponential

• Quadratic

Answer explanation

The problem involves an acceptable range around a target value, which is best represented by an absolute value inequality. Thus, the correct type of function is Absolute Value.

What Type of Function is This?

Investment Growth: John invests $1000 in a savings account that earns 5% interest compounded annually. Write an equation to represent the amount of money (A) John will have in the account after t years.

• Linear

• Absolute Value

• Exponential

• Quadratic

Answer explanation

The function representing John's investment growth is exponential because the amount increases by a percentage of the current amount each year, leading to growth that accelerates over time.

What Type of Function is This?

Medication Decay: A patient takes a 200 mg dose of medication. The amount of medication in their bloodstream decreases by half every 4 hours. Write an equation to represent the amount of medication (M) remaining in their bloodstream after h hours.

• Linear

• Absolute Value

• Exponential

• Quadratic

Answer explanation

The medication amount decreases by half every 4 hours, indicating a constant percentage decrease. This behavior is characteristic of exponential functions, where the quantity reduces by a fixed ratio over equal intervals.

What Type of Function is This?

1. Population Decline: The population of a certain endangered species is decreasing at a rate of 8% per year. If the current population is 5000, write an equation to represent the population (P) after y years.

• Linear

• Absolute Value

• Exponential

• Quadratic

Answer explanation

The population decline of 8% per year indicates a percentage decrease, which is characteristic of exponential functions. The equation can be modeled as P = 5000 * (0.92)^y, confirming it is an exponential function.

What Type of Function is This?

Projectile Motion (Height): A ball is thrown vertically upward from a height of 4 feet with an initial velocity of 60 feet per second. The height (h) of the ball after t seconds is given by the equation h=−16t2+60t+4.

• Linear

• Absolute Value

• Exponential

• Quadratic

Answer explanation

The equation h=−16t²+60t+4 is a quadratic function because it includes a term with t², indicating a parabolic shape. Quadratic functions model projectile motion, making 'Quadratic' the correct choice.