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Math  /  Algebra

QuestionGiven the function f(x)={5x+7x<05x+14x≥0f(x)=\left\{\begin{array}{ll} 5 x+7 & x<0 \\ 5 x+14 & x \geq 0 \end{array}\right.
Calculate the following values: f(−1)=□f(0)=□f(2)=□\begin{array}{l} f(-1)=\square \\ f(0)=\square \\ f(2)=\square \end{array}

Studdy Solution

STEP 1

What is this asking? We need to find out what the function f(x) f(x) equals when x x is −1-1, 00, and 22. Watch out! Be careful to use the right formula for f(x) f(x) depending on whether x x is less than 00 or greater than or equal to 00.

STEP 2

1. Evaluate f(−1) f(-1)
2. Evaluate f(0) f(0)
3. Evaluate f(2) f(2)

STEP 3

Since −1-1 is less than 00, we use the formula f(x)=5x+7 f(x) = 5x + 7 .

STEP 4

**Calculate**: Substitute −1-1 into the formula:
f(−1)=5⋅(−1)+7f(-1) = 5 \cdot (-1) + 7

STEP 5

**Simplify**:
f(−1)=−5+7=2f(-1) = -5 + 7 = 2

STEP 6

Since 00 is equal to 00, we use the formula f(x)=5x+14 f(x) = 5x + 14 .

STEP 7

**Calculate**: Substitute 00 into the formula:
f(0)=5⋅0+14f(0) = 5 \cdot 0 + 14

STEP 8

**Simplify**:
f(0)=0+14=14f(0) = 0 + 14 = 14

STEP 9

Since 22 is greater than 00, we use the formula f(x)=5x+14 f(x) = 5x + 14 .

STEP 10

**Calculate**: Substitute 22 into the formula:
f(2)=5⋅2+14f(2) = 5 \cdot 2 + 14

STEP 11

**Simplify**:
f(2)=10+14=24f(2) = 10 + 14 = 24

STEP 12

The values of the function are: - f(−1)=2 f(-1) = 2 - f(0)=14 f(0) = 14 - f(2)=24 f(2) = 24

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