Questions: What type of function is this? Using the table of values, find the following: a. f(-3) b. f(20) c. f(8) d. f(-1) e. If f(x)=9, what is x? f. If f(x)=4, what is x? g. If f(x)=0, what is x? h. If f(x)=-5, what is x? Sometimes, instead of finding the value of the function at a given x-value, you will be given the value of the function and asked to find the value of x. In these cases, replace the function notation and solve rather than the x. (Use the functions defined in the above examples.) a. Let f(x)=2x-3. If f(x)=15, find x. b. Let g(x)=3x+2. If g(x)=11, find x. c. Let w(x)=3x-7. If w(x)=14, find x. d. Let h(x)=-2x-5. If h(x)=-25, find x.

What type of function is this? Using the table of values, find the following: a. f(-3) b. f(20) c. f(8) d. f(-1) e. If f(x)=9, what is x? f. If f(x)=4, what is x? g. If f(x)=0, what is x? h. If f(x)=-5, what is x? Sometimes, instead of finding the value of the function at a given x-value, you will be given the value of the function and asked to find the value of x. In these cases, replace the function notation and solve rather than the x. (Use the functions defined in the above examples.) a. Let f(x)=2x-3. If f(x)=15, find x. b. Let g(x)=3x+2. If g(x)=11, find x. c. Let w(x)=3x-7. If w(x)=14, find x. d. Let h(x)=-2x-5. If h(x)=-25, find x.
Transcript text: What type of function is this? Using the table of values, find the following: a. $f(-3)$ b. $f(20)$ c. $f(8)$ d. $f(-1)$ e. If $f(x)=9$, what is $x$? f. If $f(x)=4$, what is $x$? g. If $f(x)=0$, what is $x$? h. If $f(x)=-5$, what is $x$? Sometimes, instead of finding the value of the function at a given $x$-value, you will be given the value of the function and asked to find the value of $x$. In these cases, replace the function notation and solve rather than the $x$. (Use the functions defined in the above examples.) a. Let $f(x)=2 x-3$. If $f(x)=15$, find $x$. b. Let $g(x)=3 x+2$. If $g(x)=11$, find $x$. c. Let $w(x)=3 x-7$. If $w(x)=14$, find $x$. d. Let $h(x)=-2 x-5$. If $h(x)=-25$, find $x$.
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Solution

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Solution Steps

Step 1: Identify the function type

The function given is \( f(x) = x^2 + 5 \). This is a quadratic function.

Step 2: Fill out the table of values

Calculate the values of \( f(x) \) for \( x = -2, -1, 0, 1, 2, 3 \):

  • \( f(-2) = (-2)^2 + 5 = 4 + 5 = 9 \)
  • \( f(-1) = (-1)^2 + 5 = 1 + 5 = 6 \)
  • \( f(0) = 0^2 + 5 = 0 + 5 = 5 \)
  • \( f(1) = 1^2 + 5 = 1 + 5 = 6 \)
  • \( f(2) = 2^2 + 5 = 4 + 5 = 9 \)
  • \( f(3) = 3^2 + 5 = 9 + 5 = 14 \)
Step 3: Answer the first three questions

Using the table of values:

  1. \( f(-2) = 9 \)
  2. \( f(0) = 5 \)
  3. \( f(3) = 14 \)

Final Answer

  1. \( f(-2) = 9 \)
  2. \( f(0) = 5 \)
  3. \( f(3) = 14 \)
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