Question

5.3: function notation and graphing technology
the function b is defined by the equation b(x) = 16x + 23. use graphing technology

1. find the value of each expression

b(6) b(2.75) b(1.482)

1. solve each equation:

b(x) = 93 b(x) = 42.1 b(x) = 116.25
lesson 5 summary
knowing the rule that defines a function can be very useful. it can help us to:

• find the output when we know the input.
• if the rule f(x) = 5(x + 2) defines f, we can find f(100) by evaluating 5(100 + 2).
• if m(x) = 3 - \\(\frac{1}{2}\\)x defines function m, we can find m(10) by evaluating 3 - \\(\frac{1}{2}\\)(10).
• create a table of values.

here are tables representing functions f and m:

Explanation:

Step1: Evaluate \( B(6) \)

Substitute \( x = 6 \) into \( B(x)=16x + 23 \).
\( B(6)=16\times6 + 23=96 + 23 = 119 \)

Step2: Evaluate \( B(2.75) \)

Substitute \( x = 2.75 \) into \( B(x)=16x + 23 \).
\( B(2.75)=16\times2.75+23 = 44+23 = 67 \)

Step3: Evaluate \( B(1.482) \)

Substitute \( x = 1.482 \) into \( B(x)=16x + 23 \).
\( B(1.482)=16\times1.482+23=23.712 + 23 = 46.712 \)

Step4: Solve \( B(x)=93 \)

Set \( 16x + 23 = 93 \). Subtract 23 from both sides: \( 16x=93 - 23 = 70 \). Divide by 16: \( x=\frac{70}{16}=4.375 \)

Step5: Solve \( B(x)=42.1 \)

Set \( 16x + 23 = 42.1 \). Subtract 23: \( 16x=42.1 - 23 = 19.1 \). Divide by 16: \( x=\frac{19.1}{16}=1.19375 \)

Step6: Solve \( B(x)=116.25 \)

Set \( 16x + 23 = 116.25 \). Subtract 23: \( 16x=116.25 - 23 = 93.25 \). Divide by 16: \( x=\frac{93.25}{16}=5.828125 \)

Answer:

s:

1. \( B(6)=\boldsymbol{119} \), \( B(2.75)=\boldsymbol{67} \), \( B(1.482)=\boldsymbol{46.712} \)
2. For \( B(x) = 93 \), \( x=\boldsymbol{4.375} \); for \( B(x)=42.1 \), \( x=\boldsymbol{1.19375} \); for \( B(x)=116.25 \), \( x=\boldsymbol{5.828125} \)