2 Functions as Mathematical Models Online Quiz Questions

A quantity increases by a factor of 1.05 for every one-unit increase in time. Which function family is the most appropriate model?

True or false: A relation is a function if every permitted input is assigned exactly one output.

True or false: For the piecewise parking-garage function in the material, the value at $t=2$ is found using the rule $C(t)=5$.

What test determines whether a graph represents a function by checking whether any vertical line intersects the graph more than once?

Select all statements that describe general rules that can restrict the real-valued domain of a function.

What is the vertex of $g(x)=-2(x-3)^2+5$?

For the model $A(t)=500(1.08)^t$, select all statements that are correct.

Using $T(d)=72-0.5d$, what temperature is predicted at a depth of 20 meters? Enter the value in degrees Celsius. The absolute tolerance is 0, so enter the exact value.

A gym charges a one-time enrollment fee of $25 and $18 per month for the first year. Construct a function model for the total cost, define the variables, state a meaningful domain, and interpret both constants. Explain why a linear model is appropriate.

A taxi fare is modeled by $C(m)=3+2m$, where $m$ is the number of miles traveled and $C(m)$ is the cost. Which quantity is the input of the model?

A population is modeled by $P(t)=120+15t$, where $t$ is measured in years. What does the constant 120 represent?

The account model $A(t)=500(1.08)^t$ describes growth over time. What does the factor $1.08$ represent?

A parking garage charges $C(t)=5$ for $0\le t\le2$ and $C(t)=5+3(t-2)$ for $t>2$. What is $C(3)$?

True or false: A graph represents a function if every vertical line intersects the graph at no more than one point.

For $g(x)=-2(x-3)^2+5$, enter the x-coordinate of the vertex.

A quantity increases by 6% during every equal time interval. Which function family is the most appropriate possible model?

The temperature model $T(d)=72-0.5d$ is intended for depths from 0 meters through 40 meters. Which domain is meaningful for this model?

For $g(x)=\log_2(x+4)-1$, which equation gives the vertical asymptote?