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Questions and Answers
What is the value of $2^5 - 3(4 + 5)$?
What is the value of $2^5 - 3(4 + 5)$?
Simplify the expression: $3x^2 - 5x + 2$, when $x = -2$?
Simplify the expression: $3x^2 - 5x + 2$, when $x = -2$?
If $f(x) = 2x^2 - 3x + 5$, what is the value of $f(3)$?
If $f(x) = 2x^2 - 3x + 5$, what is the value of $f(3)$?
What is the solution to the equation $5x - 3 = 2x + 7$?
What is the solution to the equation $5x - 3 = 2x + 7$?
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If $g(x) = 4x^2 + 2x - 6$, what is the value of $g(-2)$?
If $g(x) = 4x^2 + 2x - 6$, what is the value of $g(-2)$?
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What is the value of $4(3x - 2) - 2(2x + 1)$ when $x = 4$?
What is the value of $4(3x - 2) - 2(2x + 1)$ when $x = 4$?
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Study Notes
Algebraic Expressions and Equations
Evaluating Expressions
- To evaluate an expression, substitute the given value of the variable into the expression.
- Example: Evaluate the expression $3x^2 - 5x + 2$ when $x = -2$.
- Replace $x$ with $-2$ in the expression.
- Calculate the value of the expression: $3(-2)^2 - 5(-2) + 2 = 3(4) + 10 + 2 = 12 + 10 + 2 = 24$
Function Values
- A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range).
- To find the value of a function, substitute the input value into the function.
- Examples:
- Find the value of $f(x) = 2x^2 - 3x + 5$ when $x = 3$.
- Replace $x$ with $3$ in the function: $f(3) = 2(3)^2 - 3(3) + 5 = 2(9) - 9 + 5 = 18 - 9 + 5 = 14$
- Find the value of $g(x) = 4x^2 + 2x - 6$ when $x = -2$.
- Replace $x$ with $-2$ in the function: $g(-2) = 4(-2)^2 + 2(-2) - 6 = 4(4) - 4 - 6 = 16 - 4 - 6 = 6$
Solving Equations
- An equation is a statement that two expressions are equal.
- To solve an equation, isolate the variable on one side of the equation.
- Example: Solve the equation $5x - 3 = 2x + 7$.
- Add 3 to both sides: $5x = 2x + 10$
- Subtract 2x from both sides: $3x = 10$
- Divide both sides by 3: $x = 10/3$
Simplifying Expressions
- Simplify the expression $4(3x - 2) - 2(2x + 1)$ when $x = 4$.
- Expand the expression: $12x - 8 - 4x - 2 = 8x - 10$
- Substitute $x = 4$ into the simplified expression: $8(4) - 10 = 32 - 10 = 22$
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Description
Test your knowledge of expressions and functions with these multiple-choice questions. Practice simplifying expressions and finding the values of functions at given points.
