Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

The problem asks us to draw the graph of $g(x) = f(x) - 4$ in the first coordinate grid and $g(x) = ...

Graph TransformationsFunctionsVertical ShiftHorizontal Shift
2025/6/12

We are given that the point $(8, -5)$ lies on the graph of $f(x)$. We are also given the transformat...

FunctionsTransformations of FunctionsGraphing
2025/6/12

We are given the transformed function $f(x) = \frac{1}{8}h(x-6)-5$ and we want to determine the tran...

Function TransformationsVertical CompressionVertical ShiftHorizontal Shift
2025/6/12

The problem asks to identify the transformations applied to the parent function $h(x)$ to obtain the...

Function TransformationsTransformations of GraphsReflectionVertical StretchVertical Shift
2025/6/12

The problem asks to identify the type of transformation applied to the parent function $g(x)$ to obt...

Function TransformationsVertical ShiftsFunction Analysis
2025/6/12

We are given the transformed function $f(x) = -3h(x - 4) - 2$, and we need to determine the transfor...

Function TransformationsTransformations of FunctionsParent FunctionsVertical StretchReflectionHorizontal ShiftVertical Shift
2025/6/12

The problem consists of three statements regarding transformations of functions. The task is to iden...

Function TransformationsGraphingHorizontal ShiftVertical ShiftVertical Stretch
2025/6/12

The problem defines a function $g(\theta)$ in terms of a determinant $f(\theta)$. We are given $g(\t...

DeterminantsTrigonometryQuadratic EquationsOptimizationInequalities
2025/6/11

The problem states that for every 4 days and 3 nights of work, a person earns 8 dollars. The questio...

Linear EquationsWord ProblemSystems of Equations
2025/6/11

The problem asks to find the sum $S_n$ of the following two series: (1) $1 \cdot 3, 3 \cdot 5, 5 \cd...

SeriesSummationSequencesAlgebraic Manipulation
2025/6/11