Question

1 multiple choice 1 point compared to its “parent” function f(x)=x², what effect will we see in the graph of f(x) - 3? translated 3 units down translated 3 units up translated 3 units left translated 3 units right 2 multiple choice 1 point what is the range of the function f(x)=2x + 3 when the domain is {-3,-1,1}? {3,-1,-5} {-3,1,5} {3,1,5} {9,5,3} 3 multiple choice 1 point compared to its “parent” function f(x)=x², what effect will we see in the graph of f(x - 4)? translated 4 units down translated 4 units up translated 4 units right

Explanation:

Step1: Recall function - translation rules

For a function \(y = f(x)\), \(y=f(x)-k\) (where \(k>0\)) is a vertical - shift down by \(k\) units. For \(y = f(x)\), \(y = f(x - h)\) (where \(h>0\)) is a horizontal - shift right by \(h\) units. To find the range given the domain, substitute domain values into the function.

Step2: Solve question 1

The parent function is \(f(x)=x^{2}\), and the new function is \(f(x)-3=x^{2}-3\). According to the vertical - shift rule, the graph of \(y = f(x)-3\) is the graph of \(y = f(x)\) translated 3 units down.

Step3: Solve question 2

The function is \(f(x)=2x + 3\) and the domain is \(\{-3,-1,1\}\).
When \(x=-3\), \(f(-3)=2\times(-3)+3=-6 + 3=-3\).
When \(x=-1\), \(f(-1)=2\times(-1)+3=-2 + 3=1\).
When \(x = 1\), \(f(1)=2\times1+3=2 + 3=5\). So the range is \(\{-3,1,5\}\).

Step4: Solve question 3

The parent function is \(f(x)=x^{2}\), and the new function is \(f(x - 4)=(x - 4)^{2}\). According to the horizontal - shift rule, the graph of \(y = f(x - 4)\) is the graph of \(y = f(x)\) translated 4 units right.

Answer:

1. translated 3 units down
2. \(\{-3,1,5\}\)
3. translated 4 units right