🧮 algebra

1. **State the problem:** We want to find where the equation $f(x) = g(x)$ has a solution based on the given table values for $f(x) = 2.5x + 2$ and $g(x) = 4^{x - 2}$.\n\n2. **Reca

1. **Nyatakan masalah / State the problem:** Diberi graf fungsi $$f(x) = ax^n + c$$ dengan titik vertex di $$(0, 3)$$ dan titik lain di $$(-3, 21)$$.

1. **Nyatakan masalah:** Selesaikan persamaan kuadratik $$-\frac{k}{k - 2} = \frac{4}{k + 3}$$. 2. **Langkah pertama:** Darabkan kedua-dua belah persamaan dengan penyebut bersama i

1. Este contenido corresponde a la Unidad 1: "Álgebra y funciones" para grado 9no. 2. Se estudian los conjuntos numéricos: números racionales, irracionales y reales, y sus operacio

1. **Problem Statement:** We are given the line through points A and C as $$y = 3x + 9$$ and several questions about the parabola, lines, intersections, gradients, and domains.

1. The problem is to find the square root of 81. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. **State the problem:** Simplify the expression $$3x - 6$$ or factor it if possible. 2. **Formula and rules:** To factor an expression, look for the greatest common factor (GCF)

1. **State the problem:** We need to construct a rational function $f(x) = \frac{P(x)}{Q(x)}$ that satisfies:

1. **State the problem:** We need to construct a degree 6 polynomial function $f(x)$ with zeros at $x=-1$ (multiplicity 3), $x=2$ (multiplicity 2), and $x=-4$ (multiplicity 1). The

1. **State the problem:** We analyze the function $$g(x) = \frac{(x+1)^2(x-4)}{(x+1)(x^2 -16)}$$ including factoring, domain, asymptotes, holes, intercepts, sign, and graph.

1. **State the problem:** We analyze the rational function $$R(x) = \frac{x^2 + 2x - 8}{x^2 - 16}$$ to find its domain, vertical asymptotes, holes, horizontal/oblique asymptotes, i

1. **Nyatakan masalah:** Kita diberikan komposisi fungsi $$(g \circ f)(x) = x^2 + 2x + 3$$ dan fungsi $$f(x) = x + 1$$. Kita diminta menentukan fungsi $$g(x)$$. 2. **Gunakan defini

1. **Nyatakan masalah:** Kita diberikan komposisi fungsi $$(f \circ g)(x) = 4x + 7$$ dan fungsi $$g(x) = 2x + 1$$. Kita diminta mencari fungsi $$f(x)$$. 2. **Ingat definisi komposi

1. **State the problem:** We analyze the polynomial function $$f(x) = -2x^3(x + 1)^2(x - 3)$$ to find zeros, multiplicities, intercepts, end behavior, turning points, and sketch th

1. **Nyatakan masalah:** Kita diminta membuat dua fungsi $f$ dan $g$ yang berbeda sehingga komposisi fungsi $f \circ g$ tidak sama dengan $g \circ f$.

1. **Nyatakan masalah:** Diberikan fungsi $f(x) = x^2$ dan $g(x) = 2x + 1$, kita diminta menentukan komposisi fungsi $(g \circ f)(x)$.

1. **Nyatakan masalah:** Diberikan fungsi $f(x) = x + 2$ dan $g(x) = 3x - 1$. Kita diminta menentukan komposisi fungsi $(f \circ g)(x)$. 2. **Definisi komposisi fungsi:** Komposisi

1. **State the problem:** We want to divide the polynomial $$x^4+2x^3-4x^2-10x+5$$ by $$x^2-5$$ using synthetic division. 2. **Note:** Synthetic division is typically used for divi

1. **Menentukan fungsi komposisi $g \circ f$ dan $f \circ g$** Diketahui:

1. **Menentukan $(f \circ g)(x)$** - Masalah: Kita ingin mencari $f(g(x))$.

1. **Memahami masalah:** Kita punya dua fungsi jarak, $f(x) = 2x + 3$ dari rumah ke sekolah dan $g(x) = x + 4$ dari sekolah ke perpustakaan. 2. **Menentukan fungsi komposisi $g \ci