devyy Understanding the Domain of a Function The domain of a function represents all the possible input values (often referred to as x values) that the function can accept. To find the domain of a function from its graph, follow these steps: 1. Analyze the Graph Look closely at the graph you’re given. Start by identifying … Read more
The end behavior of a polynomial function like f(x) = 3x^4 + x^3 – 2x^2 + 4x – 5 is primarily determined by its leading term, which is the term with the highest degree. In this case, the leading term is 3x^4. As x approaches positive infinity (x → +∞): Since the leading term 3x^4 … Read more
The highest common factor (HCF) is the largest positive integer that divides each of the given numbers without leaving a remainder. Let’s analyze the numbers 1, 2, and 12 to determine their HCF. 1. **Factors of 1:** The only factor of 1 is 1 itself. 2. **Factors of 2:** The factors of 2 are 1 … Read more
To find the differential of the function \(f(t, u, v, w) = t v^6 u v w\), we need to understand how to apply the rules of differentiation with respect to multiple variables. The differential of a function \(f\) with respect to its variables can be expressed as: \[ df = \frac{\partial f}{\partial t} dt … Read more
The sum of a geometric sequence can be calculated using the formula: Sn = a1 × rac{(1 – r^n)}{1 – r} Where: Sn is the sum of the first n terms. a1 is the first term of the sequence. r is the common ratio between the terms. n is the number of terms. In your … Read more
Determining the Quotient of the Polynomial Division To find the quotient of the polynomial x³ + 3x² + 5x + 3 when divided by x + 1, we will use polynomial long division. Step-by-Step Polynomial Long Division Setup: Write x³ + 3x² + 5x + 3 inside the division symbol and x + 1 outside. … Read more
A decagon is a ten-sided polygon, and calculating the number of diagonals that can be drawn from each vertex requires some basic understanding of geometry. The formula for finding the number of diagonals from one vertex of a polygon is: Diagonals from one vertex = Total vertices – 3 This is because a vertex cannot … Read more
To rewrite the quadratic function f(x) = x² + 10x – 7 in vertex form, we can follow the completing the square method. Step 1: Identify the coefficients We start with the equation in the standard form: f(x) = x² + 10x – 7 Here, the coefficient of the x² term is 1, and the … Read more
To solve this problem, we start by understanding the concept of inverse variation. If a varies inversely as b, it means that as one of the variables increases, the other decreases. Mathematically, this relationship can be represented as: a × b = k where k is a constant. 1. **Determine the constant (k):** Given that … Read more
The term ‘locus’ is derived from Latin, meaning ‘place’ or ‘location’. In various fields, ‘locus’ can have specific and nuanced meanings: In Mathematics: A locus refers to a set of points that satisfies a particular condition or a set of conditions. For example, in coordinate geometry, the locus of points equidistant from a given point … Read more