Given f(x)=3x^2+5x-3 what are the range values when the domain is -2,0,1 -1,5 -3,-1,5 -5,1,3 -25,-3,5

## Step 1: Define the problem<br />### The goal is to find the range values of the function $f(x) = 3x^2 + 5x - 3$ for each given domain set. To do this, we substitute each value from the domain into the function and calculate the corresponding $f(x)$ values.<br /><br />## Step 2: Calculate range for $\{-2, 0, 1\}$<br />### Substitute $x = -2$, $x = 0$, and $x = 1$ into $f(x)$:<br />- For $x = -2$: $f(-2) = 3(-2)^2 + 5(-2) - 3 = 12 - 10 - 3 = -1$<br />- For $x = 0$: $f(0) = 3(0)^2 + 5(0) - 3 = -3$<br />- For $x = 1$: $f(1) = 3(1)^2 + 5(1) - 3 = 3 + 5 - 3 = 5$<br />### Range: $\{-3, -1, 5\}$<br /><br />## Step 3: Calculate range for $\{-1, 5\}$<br />### Substitute $x = -1$ and $x = 5$ into $f(x)$:<br />- For $x = -1$: $f(-1) = 3(-1)^2 + 5(-1) - 3 = 3 - 5 - 3 = -5$<br />- For $x = 5$: $f(5) = 3(5)^2 + 5(5) - 3 = 75 + 25 - 3 = 97$<br />### Range: $\{-5, 97\}$<br /><br />## Step 4: Calculate range for $\{-3, -1, 5\}$<br />### Substitute $x = -3$, $x = -1$, and $x = 5$ into $f(x)$:<br />- For $x = -3$: $f(-3) = 3(-3)^2 + 5(-3) - 3 = 27 - 15 - 3 = 9$<br />- For $x = -1$: $f(-1) = 3(-1)^2 + 5(-1) - 3 = 3 - 5 - 3 = -5$<br />- For $x = 5$: $f(5) = 3(5)^2 + 5(5) - 3 = 75 + 25 - 3 = 97$<br />### Range: $\{-5, 9, 97\}$<br /><br />## Step 5: Calculate range for $\{-5, 1, 3\}$<br />### Substitute $x = -5$, $x = 1$, and $x = 3$ into $f(x)$:<br />- For $x = -5$: $f(-5) = 3(-5)^2 + 5(-5) - 3 = 75 - 25 - 3 = 47$<br />- For $x = 1$: $f(1) = 3(1)^2 + 5(1) - 3 = 3 + 5 - 3 = 5$<br />- For $x = 3$: $f(3) = 3(3)^2 + 5(3) - 3 = 27 + 15 - 3 = 39$<br />### Range: $\{5, 39, 47\}$<br /><br />## Step 6: Calculate range for $\{-25, -3, 5\}$<br />### Substitute $x = -25$, $x = -3$, and $x = 5$ into $f(x)$:<br />- For $x = -25$: $f(-25) = 3(-25)^2 + 5(-25) - 3 = 1875 - 125 - 3 = 1747$<br />- For $x = -3$: $f(-3) = 3(-3)^2 + 5(-3) - 3 = 27 - 15 - 3 = 9$<br />- For $x = 5$: $f(5) = 3(5)^2 + 5(5) - 3 = 75 + 25 - 3 = 97$<br />### Range: $\{9, 97, 1747\}$