12.1: Math Talk: A Negative Input
Evaluate each expression when \(x\) is -5:
12.2: Equations and Their Graphs
Two students are evaluating \(x^2+7\) when \(x\) is -3. Here is their work. Do you agree with either of them? Explain your reasoning.
Evaluate each expression when \(x\) is -4:
- \(\frac12 x^2\)
- \(\text-\frac18 x^2\)
Using graphing technology, graph \(y = x\). Then, experiment with the following changes to the function. Record your observations (include sketches, if helpful).
- Adding different constant terms to \(x\) (for example: \(x + 4\), \(x - 3\)).
- Multiplying \(x\) by different positive coefficients greater than 1 (for example: \(6x, 2.5x\)).
- Multiplying \(x\) by different positive coefficients between 0 and 1 (for example: \(0.25x, 0.1x\)).
- Multiplying \(x\) by negative coefficients (for example: \(\text-9x, \text-4x\)).
Use your observations to sketch these functions on the coordinate plane, which currently shows \(y=x\).
- \(y =\text-0.5x + 2.1\)
\(y = 2.1x - 0.5\)
12.3: Match the Graphs
- Evaluate each expression when \(x\) is -3.
- For each graph, come up with an equation that the graph could represent. Verify your equation using graphing technology.