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 \(h(x) = 3(x-1)^2\).

Graph of three functions on coordinate plane, no grid. Horizontal x axis from negative 2 to 4, by 2’s. Vertical y axis from 0 to 30, by 10’s. Green function, top, passes through negative 2 comma 27, negative 1 comma 12, 0 comma 3, 1 comma 0, 2 comma 3, 3 comma 12 and 4 comma 27. Blue function, center, passes through negative 2 comma 18, negative 1 comma 8, 0 comma 2, 1 comma 0, 2 comma 2, 3 comma 8 and 4 comma 18. Black function, bottom, passes through negative 2 comma 9, negative 1 comma 4, 0 comma 1, 1 comma 0, 2 comma 1, 3 comma 4, and 4 comma 9.

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?