Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

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

The sum of the first 3 terms of a sequence is 9. The sum of the first 6 terms is -63. Given that thi...

Arithmetic SequencesLinear EquationsSystems of Equations
2025/6/11

The problem has three parts: (a) Factorize completely $2\pi h + 2\pi r^2$. (b) Express $\frac{4}{x+5...

FactorizationRational ExpressionsSimultaneous EquationsLinear Equations
2025/6/11

The problem is to solve the following five linear equations: 1. $8 - 8x = 9 - 9x$

Linear EquationsSolving Equations
2025/6/10

The problem is about the quadratic function $y = -2x^2 + (a+3)x + a - 3$. (1) Find the condition on ...

Quadratic FunctionsDiscriminantVieta's FormulasVertex of ParabolaIsosceles Right Triangle
2025/6/10

The problem consists of several sub-problems covering various topics in algebra. These include expre...

Scientific NotationEngineering NotationSimplificationPolynomial Remainder TheoremSimultaneous EquationsLogarithmic EquationsLinear EquationsGradientY-interceptEquation of a LinePartial Fractions
2025/6/10