Lesson 11

A line \(\ell\) is defined by the equation \(f(x) = 2x - 3\).

1. Line \(m\) is the same as line \(l\), but shifted 1 unit right. What is an equation for a function \(g\) that defines the line \(m\)?
2. Line \(n\) is the same as line \(m\), but shifted 2 units up. What is an equation for a function \(h\) that defines the line \(n\)?
3. What is the relationship between \(f\) and \(h\)?

The functions \(g\) and \(f\) are related by the equation \(g(x) = f(\text-x) + 3\). Which sequence of transformations will take the graph of \(f\) to the graph of \(g\)?

The function \(f\) is linear. Can \(f\) be an odd function? Explain how you know

Technology required. The function \(f\) is given by \(f(x) = x^3 + 1\). Kiran says that \(f\) is odd because \((\text-x)^3 = \text-x^3\). 

1. Do you agree with Kiran? Explain your reasoning.
2. Graph \(f\), and use the graph to decide whether or not \(f\) is an odd function. 

Here are graphs of three functions \(f\), \(g\), and \(h\) given by \(f(x) = (x-1)^2\), \(g(x) = 2(x-1)^2\) and \(h(x) = 3(x-1)^2\).

Identify which function matches each graph. Explain how you know.

Technology required. Describe how to transform the graph of \(f(x) = x^2\) into the graph of \(g(x) = 4(3x-1)^2 + 5\). Check your response by graphing \(f\) and \(g\).

Let \(p\) be the price of a T-shirt, in dollars. A company expects to sell \(f(p)\) T-shirts a day where \(f(p) = 50 - 4p\). Write a function \(r\) giving the total revenue received in a day.

A population of 80 single-celled organisms is tripling every hour. The population as a function of hours since it is measured, \(h\), can be represented by \(g(h) =80 \boldcdot 3^h\).

Which equation represents the population 10 minutes after it is measured?

\(g(10) =80 \boldcdot 3^{10}\)

\(g(0.1) =80 \boldcdot 3^{0.1}\)

\(g(\frac16) =80 \boldcdot 3^\frac16\)

\(g(6) =80 \boldcdot 3^6\)