Review for Math 1111 Final Exam

Front

What is the y-intercept of the function y=4^(x+1)?

Back

The y-intercept is the point where the graph intersects the y-axis. For the function y=4^(x+1), the y-intercept occurs when x=0, giving y=4^(0+1)=4. Thus, the y-intercept is (0,4).

Front

How do you solve the inequality |x + 4| - 8 > 2?

Back

To solve |x + 4| - 8 > 2, first isolate the absolute value: |x + 4| > 10. This leads to two cases: x + 4 > 10 or x + 4 < -10. Solving these gives x > 6 or x < -14.

Front

What is the domain of the function f(x) = 3x/(x+3)?

Back

The domain of a function is the set of all possible input values (x) that will not cause division by zero. For f(x) = 3x/(x+3), the denominator x+3 cannot be zero, so x cannot be -3. Therefore, the domain is (-∞, -3) ∪ (-3, ∞).

Front

How do you evaluate f(x) - g(x) for f(x) = 3x + 8 and g(x) = x + 8?

Back

To evaluate f(x) - g(x), subtract the two functions: f(x) - g(x) = (3x + 8) - (x + 8) = 3x + 8 - x - 8 = 2x.

Front

What is the maximum height of an object launched upward with the function s(t) = -16t^2 + 64t + 80?

Back

To find the maximum height, use the vertex formula t = -b/(2a) for the quadratic equation s(t). Here, a = -16 and b = 64. Thus, t = -64/(2*-16) = 2 seconds. Plugging t back into s(t) gives s(2) = -16(2^2) + 64(2) + 80 = 144 ft.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output (y) for each input (x). It can be represented as f(x), where x is the input and f(x) is the output.

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph. Formally, a function f is continuous at a point x=a if lim (x→a) f(x) = f(a).

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function has the form f(x) = mx + b, where m and b are constants, and its graph is a straight line. A quadratic function has the form f(x) = ax^2 + bx + c, where a, b, and c are constants, and its graph is a parabola.

Front

How do you find the x-intercepts of a function?

Back

To find the x-intercepts of a function, set f(x) = 0 and solve for x. The solutions are the points where the graph intersects the x-axis.

Front

What is the vertex of a parabola given by the equation y = ax^2 + bx + c?

Back

The vertex of a parabola can be found using the formula x = -b/(2a). The y-coordinate can be found by substituting this x value back into the equation.