Polynomial and Rational Functions
If represents a vertically stretched quadratic function, what is true about its vertex compared to that of ?
It has not shifted but is reflected over the y-axis due to multiplication by -2.
It is shifted right by five and up by seven with reflection across x-axis due to multiplication by -2.
It is shifted left by five and down by seven with no reflection across any axis.
It is shifted right by five and down seven with reflection across y-axis due to multiplication of x-coordinates by -1/5.
If an object's height above ground over time can be modeled by , what must equal if it takes exactly three seconds for the object to hit the ground after being launched from an initial height of zero?
v₀=-64 feet per second
v₀=32 feet per second
v₀=96 feet per second
v₀=48 feet per second
If the leading coefficient of a polynomial function is doubled, how does this affect the end behavior of the graph?
The graph becomes steeper and approaches infinity or negative infinity more rapidly.
There will be a vertical stretch by a factor of two in the whole graph.
The x-intercepts of the graph are shifted horizontally.
The end behavior does not change.
Given the function , where a and b are constants, if the rate of change of is always positive, what can we say about the values of a and b?
The value of a must be less than or equal to zero, while b must be greater than zero.
The value of a must be less than or equal to zero, while b can be either positive or negative.
Both a and b must be positive.
The value of a must be greater than or equal to zero, while b can be negative.
If represents rate change original position function , then question asks identify correct interpretation given statement concerning expressions involving these functions.
Q evaluates average speed period starting ending points being considered
Q determines acceleration rate corresponding interval
Q measures instantaneous velocity object moving according P's path time T
Q calculates total distance traveled until moment T
What is the result when raising a real number to the power of zero?
One
Zero
The number itself
Negative one
Which description best matches a linear function's graph?
A straight line.
A curve that never touches the x-axis.
An oscillating wave pattern.
A U-shaped curve.

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Which of the following is a possible zero for a polynomial function?
An integer value where the graph crosses the x-axis.
A fraction greater than one where the graph touches but does not cross the x-axis.
A complex number that causes shifts in the vertical asymptote.
A negative decimal point where the graph has a local minimum.
Given the polynomial equation , which of the following could be a potential factor?
Which of the following functions has exactly one real zero?
j(x) = (x-6)^3
g(x) = (x + 4)(x - 4)
f(x) = (x - 2)^2 + 3
h(x) = (x +5)(x -5)(x-1)