Question

a gym offers after - school activities at different prices. students are charged for each session. the gymnastics class also has a $50 registration fee. the equation and table each represent the total cost, y, as a function of the number of sessions, x. dance class: y = 18x gymnastics class: (table with x: 0,1,2,3,4 and y: 50,52,54,56,58) decide whether each statement is true or false. 1. the gymnastics class has an initial value of $50. (true/false) 2. the dance class does not have an initial value of $18. (true/false) 3. each session of gymnastics costs $52. (true/false)

Explanation:

Step1: Analyze Gymnastics Class Initial Value

For the gymnastics class, when \( x = 0 \) (0 sessions), \( y = 50 \). So the initial value (registration fee) is $50. So the first statement "The gymnastics class has an initial value of $50" is True.

Step2: Analyze Dance Class Initial Value

The dance class function is \( y = 18x \). The initial value (when \( x = 0 \)) is \( y = 18(0)=0 \), not $18. So the second statement "The dance class has an initial value of $18" is False.

Step3: Analyze Gymnastics Session Cost

From the gymnastics table, when \( x \) increases by 1 (from 0 to 1), \( y \) increases by \( 52 - 50 = 2 \). So each session costs $2, not $52. So the third statement "Each session of gymnastics costs $52" is False.

Answer:

1. The gymnastics class has an initial value of $50: True
2. The dance class has an initial value of $18: False
3. Each session of gymnastics costs $52: False