Parent Functions and Transformations
This is the parent function for g(x)=sqrt(x−2)+3
What is f(x)=sqrt(x)?
Given f(x)=1/(x+1) and g(x)=x+5, this is the simplified expression for (f∘g)(x)
What is 1/(x+6)?
This is the y-intercept of the quadratic function f(x)=x2+8x+7.
What is (0,7)?
Solve for x using the One-to-One property: ln(x+3)=ln14.
What is x=11?
These are the coordinates of the point on the unit circle for the angle t=π/3.
What is (1/2,(sqrt(3))/2)?
To obtain g(x)=(x−4)2+2 from its parent function, you must shift it 4 units in this horizontal direction.
What is to the right?
This is the domain of the function g(x)=2sqrt(x).
What is [0,∞)?
For f(x)=x2−4x−21, this vertical line serves as the axis of symmetry.
What is x=2?
Use properties of logs to expand log3x4y5z2.
What is 4log3x+5log3y+2log3z?
This is the exact value of sin−1((sqrt(3))/2) in radians.
What is π/3?
This is the vertical transformation required to graph g(x)=sqrt(x+3)−4.
What is a shift 4 units down?
To find the inverse of f(x)=5x+8, you must solve for x after swapping x and y, resulting in this function.
What is f−1(x)=(x−8)/5?
This is the vertical asymptote for the rational function f(x)=(3x−6)/(x+5).
What is x=-5?
This is the vertical asymptote of the logarithmic function f(x)=ln(x−1).
What is x=1?
This is the amplitude of the trigonometric function y=−2sin8x.
What is 2?
Describe the full sequence of transformations for g(x)=(x−1)2+3.
What is a horizontal shift 1 unit right and a vertical shift 3 units up?
This is the inverse function of f(x)=x3+7.
What is f−1(x)=cubert(x−7)?
This is the horizontal asymptote for f(x)=(3x−6)/(x+5) because the degrees of the numerator and denominator are equal.
What is y=3?
Solve log2(x2−4x)=log2(5x) for x.
What is x=9 (noting x=0 is extraneous)?
Use the Law of Sines to find a missing side when A=35∘, B=40∘, and c=10.
What is side a≈5.92 or side b≈6.64?
For g(x)=sqrt(x−1)+2, this is the specific y-coordinate of the starting point of the graph.
What is 2?
Find the inverse of the rational function f(x)=(3x+8)/(x−7).
What is f−1(x)=(7x+8)/(x−3)?
The rational function f(x)=(x−3)/(x2+2x−15) has a "hole" (removable discontinuity) at this x-value.
What is x=3?
Condense this expression into a single logarithm: 1/2logx+3log(x−7).
What is log(sqrt(x)(x−7)3)?
Use the Law of Cosines to find angle A if a=7,b=5, and c=9.
What is A≈50.70∘?