To find the value of a function at a particular x-value, we simply substitute that value into the function.

We have \begin{aligned} f\left(0\right) & = 4\left(0\right) - 8 \\ & = -8 \end{aligned}

The y-intercept of a function is the point on the function where x = 0. So we know that this function has a y-intercept at \left(0, -8\right).

This means that we want to solve the equation f\left(x\right) = 0 using the expression we have for f\left(x\right).

We have \begin{aligned} f\left(x\right) & = 0 \\ 4x - 8 & = 0 \\ 4x & = 8 \\ x & = 2 \end{aligned}

The x-intercepts of a function are the points on the function where y = 0. So we know that this function has a single x-intercept at \left(2, 0\right).

We found the two intercepts in parts (a) and (b). Since two points determine a line, we can connect the intercepts to create the graph of the function.

Since x is the distance traveled in miles, we know that x > 0, which corresponds to C\left(x\right) > 2.8. We are also told that the minimum charge is \$10.

Putting these together, we have that the range is \text{Range: } \left\{y\, \vert\, y \geq 10 \right\}

The rate of change of a linear function in the form y = mx + b is m, the constant being multiplied by the variable.

In this case, the function is C\left(x\right) = 2.4x + 2.8, so the rate of change is 2.4.

Since the output of C\left(x\right) is a value in dollars, and x is a value in miles, the rate of change is 2.4 dollars per mile, and it represents the additional cost of the trip per each extra mile traveled.

We want to find the value of C\left(4\right), and compare it to the minimum cost. The larger of the two values will be the cost of Whitney's trip.

We have \begin{aligned} C\left(4\right) & = 2.4\left(4\right) + 2.8 \\ & = 9.6 + 2.8 \\ & = 12.4 \end{aligned}

Since this is larger than the minimum amount, the cost of her trip will be \$12.40.

The domain of a function is the set of all x-values that correspond to a point on the graph.

As these are linear functions, with no domain restrictions from context, all real values of x correspond to a point on each line.

So the domain of both functions is all real values of x.

The range of a function is the set of all y-values that correspond to a point on the graph.

We can see that all values of y correspond to a point on the graph of f, so its range will be all real values of y.

On the other hand, g is a constant function and so it only takes one y-value - in this case, 2. So the range of g is just y = 2.

The x-intercepts of a function are the points where it intersects the x-axis. Similarly, the y-intercept of a function is the point where it intersects the y-axis.

As these are linear functions, they will have at most one of each type of intercept.

We can see that function f crosses the x-axis at the point \left(2, 0\right), and crosses the y-axis at the point \left(0, -2\right).

Function g crosses the y-axis at the point \left(0, 2\right). Since it is a constant function, it is parallel to the x-axis and so it does not have an x-intercept.

The slope of a line is the ratio of its change in the vertical direction to the change in the horizontal direction.

That is, the slope is a measure of how far up (or down) the y-values change for each unit change in the x-values.

For function f we can see that at any point on the graph, if we move 1 unit to the right (in the x-direction), we also move 1 unit up (in the y-direction).

So the slope of f is 1.

Function g is a constant function, which has no change in its y-values. That is, at any point on the graph, moving 1 unit to the right corresponds to 0 units of change in the vertical direction.

So the slope of g is 0.