SOL Review: Analyze Graphs and Functions

Vocabulary and key concepts from the SOL Review lecture notes covering coordinate graphing, systems of equations, inequalities, quadratics, and exponential functions.

Desmos Equation Solving Strategy

You MUST use $x$ as the variable, type the equation in as you see it, and find the answer on the $x$-axis.

No Solution (Equations)

Visualized in Desmos as parallel lines when each side of the equation is typed on a separate line ($y = ext{left side}$ and $y = ext{right side}$).

Infinitely Many Solutions (Equations)

Visualized in Desmos as one line (overlapping lines) when each side of the equation is typed on a separate line.

Intersecting Lines

Indicates one solution for a system of equations, where the solution is the point of intersection.

Dashed Line ($<$ or $>$)

Used when graphing inequalities to show that solutions CANNOT be on the line.

Solid Line ($ext{≤}$ or $ext{≥}$)

Used when graphing inequalities to show that solutions CAN be on the line.

Inequality Shading Strategy

Shade right when using > or $ext{≥}$, and shade left when using < or $ext{≤}$. For systems, the solution is in the (double) shaded area.

Solutions/Zeros/Roots

Alternative names for the $x$-intercepts of a quadratic function.

Greatest Common Factor (gcf)

The largest factor shared by terms in an expression that must be included as part of the answer when factoring completely (can be found in Desmos using the gcf command).

Exponential Function

A function or equation where the variable, usually $x$, is in the exponent (e.g., $y = 2^x$).

Horizontal Asymptote

A line that an exponential function approaches; for basic functions with no vertical transformations, it is $y = 0$.

Repeating Decimals in Desmos

A strategy where you type the repeating number until the fraction button appears to convert the decimal back to its correct fraction.