Unit 7, Lesson 10
Graphs of Functions in Standard and Factored Forms
Algebra 1
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Here is a graph that represents a quadratic function.
Which expression could define this function?
A curve in an x y plane, origin O, with grid. Horizontal axis, scale negative 6 to 6, by 1’s. Vertical axis, scale negative 8 to 8, by 1’s. A curve passes through the points negative 1 comma 0, 1 comma negative 4, and 3 comma 0.
\((x+3)(x+1)\)
\((x+3)(x-1)\)
\((x-3)(x+1)\)
\((x-3)(x-1)\)
Here are graphs of functions \(f\) and \(g\), given by \(f(x) = 100 \boldcdot \left(\frac{3}{5}\right)^x\) and \(g(x) = 100 \boldcdot \left(\frac{2}{5}\right)^x\).
Which graph corresponds to \(f\) and which graph corresponds to \(g\)? Explain how you know.
Graph of two lines, origin O. Horizontal axis 0 to 6, by 1’s, labeled x. Vertical from 0 to 100, by 20’s, labeled y. Both lines start at 0 comma 100. Line A passes through 1 comma 60. Line B passes through 1 comma 40.
Here are graphs of two functions, \(f\) and \(g\).
An equation defining \(f\) is \(f(x) = 100 \boldcdot 2^x\).
Which of these could be an equation defining function \(g\)?
Graph of two increasing exponential functions, labeled f (blue) and g (green), xy-plane, origin O. The functions both start at the vertical axis, function f starts higher than function g. They appear to be very close at the upper left of the graph.
\(g(x) = 25 \boldcdot 3^x\)
\(g(x) = 50 \boldcdot (1.5)^x \)
\(g(x) = 100 \boldcdot 3^x \)
\(g(x) = 200 \boldcdot (1.5)^x\)