1.
Use the graph of the relation \(f(x)\) to determine \(f(1)\). [Image Placeholder - Q2]
Step 1. To find \(f(1)\), look for the \(y\)-value on the graph when \(x=1\). Step 2. From the graph, the point at \(x=1\) has \(y=-1\). \[f(1)=-1\] Answer: A
2.
What is the minimum number of solutions for a quintic equation?
Step 1. A quintic equation has degree \(5\). Step 2. Since \(5\) is odd, the graph of a quintic polynomial must have opposite end behavior. Step 3. This means the graph must cross the \(x\)-axis at least once. Step 4. Therefore, the minimum number of real solutions is \(1\). Answer: E
3.
If the quartic function \(y=x^4\) is represented by the green-coloured graph below, which equation best represents the translated orange-coloured graph? [Image Placeholder - Q3]
Step 1. The parent function is \(y=x^4\). Step 2. The orange graph has the same shape as \(y=x^4\), but it is translated \(5\) units down. Step 3. Moving a graph down \(5\) units means subtracting \(5\) from the function. \[y=x^4-5\] Answer: D
4.
How is the graph of \(\frac{1}{7}y=x^4\) related to the graph of \(y=x^4\)?
Step 1. Start with \(\frac{1}{7}y=x^4\). Step 2. Solve for \(y\) by multiplying both sides by \(7\). \[y=7x^4\] Step 3. Multiplying \(x^4\) by \(7\) expands the graph vertically by a factor of \(7\). Answer: D
5.
How is the graph of \(5y=2^x\) related to the graph of \(y=2^x\)?
Step 1. Start with \(5y=2^x\). Step 2. Solve for \(y\). \[y=\frac{1}{5}2^x\] Step 3. Multiplying the output of \(y=2^x\) by \(\frac{1}{5}\) compresses the graph vertically by a factor of \(\frac{1}{5}\). Answer: B
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