Algebra 1: Function Notation

Consider the function represented by the equation 6c = 2p - 10. Write the equation in function notation, where c is the independent variable. f(c) = 1/3p + 5/3 f(c) = 3c + 5 f(p) = p + f(p) = 3c + 5

f(c) = 3c + 5

The function can be used to find the volume of air inside a basketball given its radius. What does V(r) represent? the radius of the basketball when the volume is V the volume of the basketball when the radius is r the volume of the basketball when the radius is V the radius of the basketball when the volume is r

the volume of the basketball when the radius is r

Which represents a Function? (2, 3), (6, -5), (1, -3) (7, -4), (0, 9), (2, -2) (-6, 5), (-5, 6), (8, 2) (1, 9), (-3, -2), (1, -4) (0, 3), (0, 7), (4, 0)

(2, 3), (6, -5), (1, -3) (7, -4), (0, 9), (2, -2) (-6, 5), (-5, 6), (8, 2)

Marlene rides her bike at a rate of 16 miles per hour. The time in hours that she rides is represented by the variable t, and the distance she rides is represented by the variable d. Which statements are true of the scenario? Check all that apply. The independent variable, the input, is the variable d, representing distance. The distance traveled depends on the amount of time Marlene rides her bike. The initial value of the scenario is 16 miles per hour. The equation t = d + 16 represents the scenario. The function f(t) = 16t represents the scenario.

-The distance traveled depends on the amount of time Marlene rides her bike. -The function f(t) = 16t represents the scenario.

Match each function with its input. 1. g(f) = 2f 2. h(g) = -4 +g 3. f(h) = h - 7

1. The input is f 2. The input is g 3. The input is h

The population of bobcats in northern Arizona since 2008 can be modeled using the function b(t) = -0.32t2 + 2.7t + 253. What does t represent? What is the domain for this function? Which range values would not make sense for this function? Would the graph be continuous or discrete, and why?

1. The number of years since 2008 2. T values greater than or equal to 0 3. Negative values 4. Discrete, because the number of bobcats cannot be broken into fractional parts

A hot air balloon descends to the ground. The function a(t) = 210 - 15t can be used to describe the altitude of the balloon as it approaches the ground. The time is in minutes. What does t represent? What does a(t) represent? What information will a(5.5) give?

1. time after the balloon begins to descend 2. altitude of the balloon 3. altitude of the balloon after 5.5 minutes

Use the function f(x) = 2x3 - 3x2 + 7 to complete the exercises. f(−1) = f(1) = f(2) =

2 6 11

The function p(x) = -2(x - 9)2 + 100 is used to determine the profit on T-shirts sold for x dollars. What would the profit from sales be if the price of the T-shirts were $15 apiece? $15 $28 $172 $244

$28

The function h(t) = 8 - 0.5t models the height of a candle over time t. Will the graph of the function be a continuous graph or a discrete graph?

Continuous graph

How can a domain value of -3 and a corresponding range value of 0 be written using function notation?

F(-3) = 0

How can (1, -2) be written using function notation?

F(1) = -2

The equation y= 3x -4 can be written using function notation. y= the dependent variable

F(x) = 3x - 4

A tablet has 32 GB of storage available, and each video download requires 2 GB. The amount of storage left in GB is represented by the variable s, and the number of videos downloaded is represented by the variable v. Write a function that models the relationship between storage left and number of videos downloaded Input = v Output = s

T(v) = 32 - 2v

A hot air balloon descends to the ground. The function h(t) = 210 - 15t can be used to describe the altitude of the balloon as it approaches the ground. Which statement best describes the graph of the function that models the descent of the balloon? The graph is discrete because there cannot be fractional values for time. The graph is discrete because there cannot be negative values for altitude. The graph is continuous because there can be fractional values for time. The graph is continuous because there can be negative values for altitude.

The graph is continuous because there can be fractional values for time.

What does f(x) = 7 mean?

The output of f is 7 when the input is 1.

What is the meaning of f(x)? ("f of x")

The output value of f when the input value is x.

What is true of the function g(x) = -2x^2 + 5? g(x) is the multiplication of g and x. -2x2 +5 is the input of the function. The variable x represents the independent variable. The variable g represents the input of the function.

The variable x represents the independent variable.

Domain: ___________ Range:____________

The x values The y values

In a function, each value for the independent variable (input values) maps to, or corresponds to, exactly one value for the dependent variable (output values). True False

True

The point (-3, -5) is on the graph of a function. Which equation must be true regarding the function? f(-3) = -5 f(-3, -5) = -8 f(-5) = -3 f(-5, -3) = -2

f(-3) = -5

Andrea conducts a science experiment and observes that the height of a plant depends on the amount of sunlight it receives. The plant's height is 37 centimeters, and it grows at a rate of 0.004 centimeter per hour of sunlight. If the number of hours of sunlight is represented by the variable s, which function can represent the height of the plant? s(h) = 0.004h - 37 f(h) = 37h + 0.004 f(s) = 0.004s + 37

f(s) = 0.004s + 37

Which statements are true for the functions g(x) = x2 and h(x) = -x2 ? Check all that apply. For any value of x, g(x) will always be greater than h(x). For any value of x, h(x) will always be greater than g(x). g(x) > h(x) for x = -1. g(x) < h(x) for x = 3. For positive values of x, g(x) > h(x). For negative values of x, g(x) > h(x).

g(x) > h(x) for x = -1. For positive values of x, g(x) > h(x). For negative values of x, g(x) > h(x).

Which statement best describes the function h(t) = 210 - 15t? h is the function name; h(t) is the input, or independent variable; and t is the output, or dependent variable. h is the function name; t is the input, or independent variable; and h(t) is the output, or dependent variable. t is the function name; h(t) is the input, or independent variable; and h is the output, or dependent variable. t is the function name; h is the input, or independent variable; and h(t) is the output, or dependent variable.

h is the function name; t is the input, or independent variable; and h(t) is the output, or dependent variable.

An 8 inch candle burns at a rate of 0.5 inches every hour. Write a function that models the relationship between the height of the candle in inches as a function of time t in hours.

h(t) = 8 - 0.5t

What is the inverse of f(x) = x + 2? h(x) = x + 2 h(x) = x - 2 h(x) = 3x - 2 h(x) = 3x - 6

h(x) = 3x - 6