Textbook Question
Determine whether each relation defines y as a function of x. Give the domain and range. See Example 5. x = y⁶
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0. Review of College Algebra
Functions
1:12 minutesProblem 45
Textbook Question
Let f(x) = -3x + 4 and g(x) = -x² + 4x + 1. Find each of the following. Simplify if necessary. See Example 6. ƒ(0)
Verified step by step guidance1
Identify the function f(x) given as \(f(x) = -3x + 4\).
To find \(f(0)\), substitute \(x = 0\) into the function \(f(x)\).
Perform the substitution: \(f(0) = -3(0) + 4\).
Simplify the expression by multiplying and adding: \(f(0) = 0 + 4\).
Write the simplified result for \(f(0)\).
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Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Function Evaluation
Function evaluation involves substituting a given input value into the function's formula and simplifying to find the output. For example, to find f(0), replace x with 0 in f(x) and simplify the expression.
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Linear Functions
A linear function has the form f(x) = mx + b, where m is the slope and b is the y-intercept. Understanding its structure helps in quickly evaluating the function at any x-value by direct substitution.
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Quadratic Functions
A quadratic function is a polynomial of degree two, typically written as g(x) = ax² + bx + c. Evaluating it requires substituting the input value into the expression and simplifying, often involving squaring the input.
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