Solving Functions from Word Problems - SAT Subject Test in Math I
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At Joe's pizzeria a pizza costs $5 with the first topping, and then an additional 75 cents for each additional topping.
If 
represents the number of toppings on a pizza, what function represents the cost of a pizza with at least one topping?
At Joe's pizzeria a pizza costs $5 with the first topping, and then an additional 75 cents for each additional topping.
If
Notice that the question describes a linear equation because there is a constant rate of change (the cost per topping). This means we can use slope intercept form to describe the scenario.
Recall that slope intercept form is
The value of 
is the 
-value when 
. In this case 
means there are zero additional toppings and the question tells us that this pizza costs $5 so:
is the slope, or rate of change as 
increases. In this case each additional topping costs 
cents. Notice that the units have shifted from dollars to cents so we must write this as 
Notice that the first topping is included in the $5 cost. The 
cent charge only applies to additional toppings. So one less than the number of toppings is equivalent to:
Putting all these steps together we get:
Notice that the question describes a linear equation because there is a constant rate of change (the cost per topping). This means we can use slope intercept form to describe the scenario.
Recall that slope intercept form is
The value of
Notice that the first topping is included in the $5 cost. The
Putting all these steps together we get:
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