Example Question #1 : Functional Relationship Between Two Quantities
A restaurant sets the prices of its dishes using the following function:
Price = (Cost of Ingredients) + (40% of the Cost of Ingredients) + 5
where all quantities are in U.S. Dollars.
If the cost of ingredients for a steak dish is $14, what will the restaurant set the price of the steak dish at?
The price of the dish is a function of a single variable, the cost of the ingredients. One way to conceptualize the problem is by thinking of it in function notation. Let be the variable representing the cost of the ingredients. Let be a function of the cost of ingredients giving the price of the dish. Then, we can turn
"Price = (Cost of Ingredients) + (40% of the Cost of Ingredients) + 5"
into a regular equation with recognizable parts. Replace "Price" with and replace "cost of ingredients" with the variable .
Simplify by combining like terms ( and ) to obtain:
The cost of ingredients for the steak dish is $14, so substitute 14 for .
All that's left is to compute the answer:
So, the steak dish will have a price of $24.60.
Example Question #2 : Functional Relationship Between Two Quantities
The plot shows the graphs of five different equations. Using shape and location, determine which graphed line corresponds to the equation .
The power of and are both 1, so this is a linear equation of order 1. Therefore, the graph must be a straight line. We can eliminate A and E, since neither are straight lines.
The equation is given in the slope-intercept form, , where stands for the slope of the line and stands for the line's y-intercept. Since , the coefficient of x, is positive here, we are looking for a line that goes upwards. We can eliminate D since it goes downwards, and therefore has a negative slope.
In the given equation, the constant , which represents the y-intercept, is also positive. Therefore, the line we are looking for also must intersect the y-axis at a positive value. The graph C appears to intersect the y-axis at a negative value, whereas the graph B appears to intersect the y-axis at a positive value. Therefore, B is the corresponding graph.