Answer these 10 multiple-choice questions on solutions and graphs of equations, systems with a line and a parabola, exponential graphs and exponent rules. Each question has one correct answer. Substitute to check before you choose.
Which ordered pair is a solution of \(y=3x-4\)?
The graph shows \(y=x^{2}\) and \(y=x+2\). What are the solutions of the system?
Solve \(y=x^{2}\) and \(y=3x+4\).
How many solutions does the system \(y=x^{2}+2\) and \(y=1\) have?
What is the y-intercept of \(y=6\left(\frac{1}{2}\right)^{x}\)?
What is the horizontal asymptote of the graph of \(y=2^{x}-3\)?
What happens to \(y=3\cdot 2^{x}\) as \(x\) gets very small (large and negative)?
Which expression equals \(4^{x}\)?
An account grows by a factor of 1.08 each year. Using \(1.08^{t}=\left(1.08^{1/12}\right)^{12t}\), what is the monthly growth rate?
A ball follows \(y=-x^{2}+4x\) and lands on a ramp \(y=x\). Besides the origin, where do the paths meet?
🎉 Quiz complete!
Remember:
- Standards A-REI.D.10, A-REI.C.7, F-IF.C.7e and A-SSE.B.3c: graphs as solution sets, linear-quadratic systems, exponential graphs and rewriting exponentials.
- A point is on the graph of an equation exactly when its coordinates satisfy the equation.
- To solve a line-parabola system, set the two expressions for \(y\) equal, solve for \(x\), then find \(y\). There can be 2, 1 or 0 solutions.
- For \(y=a\cdot b^{x}\) the y-intercept is \((0,a)\), there is no x-intercept, and the x-axis is an asymptote.
- Rewrite with \(b^{mn}=(b^{m})^{n}\): \(1.15^{t}=(1.15^{1/12})^{12t}\) gives a monthly factor of about 1.0117.
See every chapter on the Algebra 1 math page.