Question

x^4 - 3x^2 + 2y - 1 is a polynomial of degree
a) 2
b) 5
c) 4
d) 3
question 7 (5 points)
for a given function f(x), the translation f(x - 2) + 3 means the function will shift
a) left 3 and downward 2.
b) right 3 and upward 2.
c) right 2 and upward 3.

Explanation:

Step1: Recall polynomial degree definition

The degree of a polynomial is the highest - power of the variable in the polynomial. In the polynomial $x^{4}-3x^{2}+2y - 1$, the powers of the terms are 4 for the term $x^{4}$, 2 for the term $-3x^{2}$, 1 for the term $2y$ (since $y=y^{1}$), and 0 for the constant term $-1$.

Step2: Identify the highest power

The highest power among these is 4.

Step3: Recall function - translation rules

For a function $y = f(x)$, the transformation $y=f(x - h)+k$ represents a horizontal and vertical shift. If $h>0$, the graph of the function shifts to the right by $h$ units, and if $k > 0$, the graph of the function shifts up by $k$ units. In the transformation $f(x - 2)+3$, $h = 2$ and $k=3$.

Answer:

C. 4
C. right 2 and upward 3.