関数の定義域と値域計算機 - ステップと例付き

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Practice More Type your Answer Verify x^2 x^{\msquare} \log_{\msquare} \sqrt{\square} \nthroot[\msquare]{\square} \le \ge \frac{\msquare}{\msquare} \cdot \div x^{\circ} \pi \left(\square\right)^{'} \frac{d}{dx} \frac{\partial}{\partial x} \int \int_{\msquare}^{\msquare} \lim \sum \infty \theta (f\:\circ\:g) f(x) ▭\:\longdivision{▭} \times \twostack{▭}{▭} + \twostack{▭}{▭} - \twostack{▭}{▭} \left( \right) \times \square\frac{\square}{\square} Take a challenge Subscribe to verify your answer Subscribe Are you sure you want to leave this Challenge? 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Go back Purchase Bundle Back to School Promotion Annual Annual - $ % OFF Annual plan One time offer for one year, then $ Go back + qb-banner-title Solutions > Functions & Line Calculator > Functions Domain & Range Calculator Topic Pre Algebra Algebra Pre Calculus Calculus Functions Line Equations Line Given Points Given Slope & Point Slope Slope Intercept Form Standard Form Distance Midpoint Start Point End Point Parallel Parallel Lines Perpendicular Perpendicular Lines Equation of a Line Given Points Given Slope & Point Perpendicular Slope Points on Same Line Functions Is a Function Domain Range Domain & Range Slope & Intercepts Vertex Periodicity Amplitude Shift Frequency Inverse Domain of Inverse Intercepts Parity Symmetry Asymptotes Critical Points Inflection Points Monotone Intervals Extreme Points Global Extreme Points Absolute Extreme Turning Points Concavity End Behavior Average Rate of Change Holes Piecewise Functions Continuity Discontinuity Values Table Function Reciprocal Function Negative Reciprocal Injective Surjective Arithmetic & Composition Compositions Arithmetics Conic Sections Circle Equation Radius Diameter Center Area Circumference Intercepts Symmetry Ellipse Center Axis Area Foci Vertices Eccentricity Intercepts Symmetry Parabola Foci Vertex Directrix Intercepts Hyperbola Center Axis Foci Vertices Eccentricity Asymptotes Intercepts Symmetry Conic Inequalities Transformation Linear Algebra Trigonometry Statistics Physics Chemistry Finance Economics Conversions Add to Chrome Get our extension, you can capture any math problem from any website Full pad x^2 x^{\msquare} \log_{\msquare} \sqrt{\square} \nthroot[\msquare]{\square} \le \ge \frac{\msquare}{\msquare} \cdot \div x^{\circ} \pi \left(\square\right)^{'} \frac{d}{dx} \frac{\partial}{\partial x} \int \int_{\msquare}^{\msquare} \lim \sum \infty \theta (f\:\circ\:g) f(x) - \twostack{▭}{▭} \lt 7 8 9 \div AC + \twostack{▭}{▭} \gt 4 5 6 \times \square\frac{\square}{\square} \times \twostack{▭}{▭} \left( 1 2 3 - x ▭\:\longdivision{▭} \right) . 0 = + y \mathrm{domain} \mathrm{range} \mathrm{inverse} \mathrm{extreme\:points} \mathrm{asymptotes} See All area asymptotes critical points derivative domain eigenvalues eigenvectors expand extreme points factor implicit derivative inflection points intercepts inverse laplace inverse laplace partial fractions range slope simplify solve for tangent taylor vertex geometric test alternating test telescoping test pseries test root test Go Steps Graph Related Examples Generated by AI AI explanations are generated using OpenAI technology. AI generated content may present inaccurate or offensive content that does not represent Symbolab's view. Verify your Answer Subscribe to verify your answer Subscribe Save to Notebook! Sign in to save notes Sign in Verify Save Show Steps Hide Steps Number Line Related Functions Domain & Range Examples domain\:and\:range\:y=\frac{x^2+x+1}{x} domain\:and\:range\:f(x)=x^3 domain\:and\:range\:f(x)=\ln (x-5) domain\:and\:range\:f(x)=\frac{1}{x^2} domain\:and\:range\:y=\frac{x}{x^2-6x+8} domain\:and\:range\:f(x)=\sqrt{x+3} domain\:and\:range\:f(x)=\cos(2x+5) domain\:and\:range\:f(x)=\sin(3x) Show More All About Function Domain and Range Calculator Every function has a story. It takes an input, does something to it, and gives you an output. But not just any input will work, and not every output is possible; that’s where domain and range come in. Think of it like pouring water into a bottle. You can’t pour a negative amount, and the bottle can only hold so much. The domain is what you’re allowed to pour in. The range is what you get out. In this article, we’ll take a closer look at domain and range, walk through examples together, and explore how Symbolab’s Functions Domain and Range calculator can help you see each function’s story more clearly. What Is a Function? Let’s take a moment with this. A function is one of those ideas that shows up everywhere in math, and it’s worth getting comfortable with. At its simplest, a function is a rule that takes an input, does something to it, and gives you one output. Always one. Always predictable. You can think of a function like a vending machine that works the way it should. You press a button, and it gives you exactly what that button promises. Press “B2”: you get a bag of chips. Same button, same result. That’s how a function works. One input leads to one output. No surprises. In math, we often write it like this: $f(x)$ means “the value of the function when $x$ is the input.” If the rule is $f(x) = 2x + 1$ and you plug in $x = 4$, you just follow the steps: $f(4)=2(4)+1=9$ This is all a function is: a rule you can count on. But just like not every item fits in a vending machine, not every number works in every function. Some inputs are off-limits. For example: You can’t divide by zero You can’t take the square root of a negative number (in the real number system) This is why we talk about domain and range. The domain tells you which inputs are allowed The range tells you what kinds of outputs you can get Together, they give you the full picture of what a function can do. And where it might be limited. What Is the Domain of a Function? The domain is all about what you are allowed to put into a function. In other words, it’s the set of all possible input values that make sense for that rule. Some functions let you plug in any number you like. Others have limits. The domain tells you where the function actually works. Let’s take a simple example: $f(x)=2x+3$ You can plug in any number here, positive, negative, decimal , or fraction, and it will always give you an answer. So the domain is all real numbers. Now look at this one: $g(x) = \frac{1}{x - 4}$​ You can’t divide by zero. If $x = 4$, the denominator becomes zero, and the function breaks. That means $x = 4$ is not allowed. So the domain is: all real numbers except $x = 4$. Another example: $h(x) = \sqrt{x - 2}$ You can’t take the square root of a negative number in the real number system. So we set: $x - 2 \geq 0$ which gives: $x \geq 2$ So the domain is all real numbers greater than or equal to $2$. A real-life connection Imagine you are f