IM3 midterm

Front

When f(x) = 9 - 3x and g(x) = 5x - 7, find f(x) + g(x).

Back

f(x) + g(x) = (9 - 3x) + (5x - 7) = 2x + 2.

Front

Given f(x) = 2x and g(x) = x^2 + 3, find f(g(x)).

Back

f(g(x)) = f(x^2 + 3) = 2(x^2 + 3) = 2x^2 + 6.

Front

What is the inverse of a function?

Back

The inverse of a function f(x) is a function that reverses the effect of f. If f(a) = b, then f^(-1)(b) = a.

Front

Solve for X: (x-5)(x+6)=0

Back

X = {5, -6}.

Front

Solve for x: log_4 x = 3

Back

x = 4^3 = 64.

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens.