Chapter 1 Families of graphs Name:______
Analysis task is to be completed in class as an assessment task. Please complete all work on this paper and use graph axes supplied on next page for graphing questions. Calculators are allowed and give exact answers unless requested.
A cat’s life
Domestic cats live to about 14 years on average. An often-used rule of thumb for comparing the age of a cat to a human is: 1 cat year equals about 7 human years.
a If x is the age in years of a cat and y is the corresponding human age in years, express y in terms of x using this rule of thumb.
b Graph the straight line corresponding to the rule in question a for .
In practice, the real comparison is more complicated, and there are different linear rules for different ages.
c A cat that is 1 year old has a corresponding human age of 16 years.
i Plot the point (1, 16) on the same axes as in question b and join it to (0, 0) with a straight line.
ii Write the rule for y in terms of x for .
d A cat that is 2 years old is estimated to have a corresponding human age of 22 years.
i Plot the point (2, 22) on the same axes as in question b and join it to (1, 16) with a straight line.
ii Find the gradient m of the straight line joining (1, 16) and (2, 22).
iii Find the rule connecting y and x in the form for 1 <.
iv An 18-month-old cat corresponds to what age in human years?
e Every year that a cat lives beyond the age of 2 counts as about 4 human years.
i How old in human years is a cat that survives to its average life expectancy
of 14?
ii Add a third line segment to the previous graph to show a cat’s life for all values of x.
iii Find the rule connecting y and x in the form for x > 2.
iv A centenarian is someone who is 100 years old. What is the equivalent age for a cat?
f i For what cat ages does the rule of thumb underestimate its human equivalent?
ii For what cat ages does the rule of thumb overestimate its human equivalent?
Brauer College