Pre-Calc true & false

If f and g are inverse functions, the domain of f is the same as the range of g

True

If the degree of the numerator of a rational function equals the degree of the denominator, then the ratio of the leading coefficients equals the horizontal asymptote

True

The domain of the inverse cotangent function is the set of real numbers

True

The graph of f(x)=2x^2+3x-4 opens up

True

The graph of y=-f(x) is the reflection about the x-axis of the graph y=f(x)

True

The graphs of y=tan x, y=cotx, y=secx, y=cscx each have infinitely many vertical asymptotes

True

The only even trigonometric functions are the cosine and secant functions

True

The slope of a non-vertical line is the average rate of change of the linear function

True

The x-intercepts of the graph of a function y=f(x) are the real solutions of the equations f(x)=0

True

To find the y-intercepts of the graph of an equation, let x=0 and solve for y

True

sin(-theta)+sin(theta)=0 for any value of theta

True

Most trigonometric equations have unique solutions

False

The range of exponential functions f(x)=a^x, where a>0 and a doesn't =1 is the set of all real numbers

False

The distance between two points is sometimes a negative number

False, because when you square root a number it is positive

Even functions have graphs that are symmetric with respect to the origin

False, even functions have graphs that are symmetric with respect to the y-axis

If y=logax then y=a^x

False, if y=logax then a=xy

cos(pie/2-theta)=cos theta

False, it equals sine theta

The cube root function is odd and decreasing on the interval (-infinity,infinity)

False, it is increasing on the interval

The graph of a rational function may intersect a vertical asymptote

False, it may intersect a horizontal asymptote

sec=1/sine

False, sec=1/cos

For y=2sin(3.14x), the amplitude is 2 and period is 3.14/2

False, the amplitude is 2 and the period is 2

The center of the circle (x+3)^2 + (y-2)^2 = (3,-2)

False, the center would be (-3,2)

The graph of f(x)=x/x-3 is above the x-axis for x<0 or x>3, so the solution set of the inequality x/x-3>0 is {x|x<0 or x>3}

False, the solution set would be {x|x>0 or x<3}

Perpendicular lines have slopes that are reciprocals of one another

False, they have opposite signs and their values are reciprocals

The law of sines can be used to solve triangles where three sides are known

False, you need to know two sides and one angle

The domain of the composite function (f*g)(x) is the same as the domain of g(x)

Fasle, the domain of the composite function (f*g)(x) is the same as the domain (g*f)(x)